LMFDB - Embedded newform 25.8.d.a.6.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,8,Mod(6,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			6.10
Character	$\chi$	$=$	25.6
Dual form			25.8.d.a.21.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.341871 + 1.05217i) q^{2} +(64.7040 - 47.0102i) q^{3} +(102.564 - 74.5171i) q^{4} +(265.518 + 87.3222i) q^{5} +(71.5832 + 52.0083i) q^{6} -1498.89 q^{7} +(228.032 + 165.675i) q^{8} +(1300.83 - 4003.53i) q^{9} +O(q^{10})$	\(q+(0.341871 + 1.05217i) q^{2} +(64.7040 - 47.0102i) q^{3} +(102.564 - 74.5171i) q^{4} +(265.518 + 87.3222i) q^{5} +(71.5832 + 52.0083i) q^{6} -1498.89 q^{7} +(228.032 + 165.675i) q^{8} +(1300.83 - 4003.53i) q^{9} +(-1.10492 + 309.224i) q^{10} +(1464.09 + 4505.99i) q^{11} +(3133.23 - 9643.10i) q^{12} +(-1412.50 + 4347.23i) q^{13} +(-512.427 - 1577.09i) q^{14} +(21285.1 - 6831.96i) q^{15} +(4918.16 - 15136.5i) q^{16} +(8795.02 + 6389.96i) q^{17} +4657.12 q^{18} +(-34970.7 - 25407.7i) q^{19} +(33739.6 - 10829.5i) q^{20} +(-96984.1 + 70463.1i) q^{21} +(-4240.55 + 3080.94i) q^{22} +(6401.66 + 19702.3i) q^{23} +22543.0 q^{24} +(62874.7 + 46371.2i) q^{25} -5056.93 q^{26} +(-49986.9 - 153844. i) q^{27} +(-153732. + 111693. i) q^{28} +(-45559.9 + 33101.2i) q^{29} +(14465.2 + 20059.9i) q^{30} +(127561. + 92678.3i) q^{31} +53686.2 q^{32} +(306560. + 222729. i) q^{33} +(-3716.57 + 11438.4i) q^{34} +(-397982. - 130886. i) q^{35} +(-164913. - 507551. i) q^{36} +(-82856.0 + 255005. i) q^{37} +(14777.8 - 45481.3i) q^{38} +(112970. + 347685. i) q^{39} +(46079.6 + 63902.1i) q^{40} +(143028. - 440194. i) q^{41} +(-107295. - 77954.6i) q^{42} -419904. q^{43} +(485936. + 353053. i) q^{44} +(694989. - 949418. i) q^{45} +(-18541.6 + 13471.3i) q^{46} +(-301322. + 218923. i) q^{47} +(-393347. - 1.21060e6i) q^{48} +1.42313e6 q^{49} +(-27295.5 + 82008.0i) q^{50} +869466. q^{51} +(179071. + 551125. i) q^{52} +(9133.30 - 6635.73i) q^{53} +(144781. - 105190. i) q^{54} +(-4731.88 + 1.32427e6i) q^{55} +(-341795. - 248329. i) q^{56} -3.45716e6 q^{57} +(-50403.8 - 36620.5i) q^{58} +(-561895. + 1.72933e6i) q^{59} +(1.67399e6 - 2.28682e6i) q^{60} +(-623763. - 1.91975e6i) q^{61} +(-53904.2 + 165900. i) q^{62} +(-1.94979e6 + 6.00085e6i) q^{63} +(-611171. - 1.88099e6i) q^{64} +(-754654. + 1.03093e6i) q^{65} +(-129545. + 398698. i) q^{66} +(-206291. - 149879. i) q^{67} +1.37821e6 q^{68} +(1.34042e6 + 973872. i) q^{69} +(1656.15 - 463492. i) q^{70} +(261849. - 190244. i) q^{71} +(959916. - 697420. i) q^{72} +(1.22989e6 + 3.78520e6i) q^{73} -296635. q^{74} +(6.24816e6 + 44652.4i) q^{75} -5.48004e6 q^{76} +(-2.19450e6 - 6.75399e6i) q^{77} +(-327203. + 237727. i) q^{78} +(3.44694e6 - 2.50434e6i) q^{79} +(2.62762e6 - 3.58956e6i) q^{80} +(-3.01853e6 - 2.19309e6i) q^{81} +512057. q^{82} +(-3.43591e6 - 2.49633e6i) q^{83} +(-4.69637e6 + 1.44539e7i) q^{84} +(1.77725e6 + 2.46465e6i) q^{85} +(-143553. - 441811. i) q^{86} +(-1.39181e6 + 4.28356e6i) q^{87} +(-412673. + 1.27008e6i) q^{88} +(-3.63725e6 - 1.11943e7i) q^{89} +(1.23655e6 + 406669. i) q^{90} +(2.11718e6 - 6.51602e6i) q^{91} +(2.12474e6 + 1.54371e6i) q^{92} +1.26105e7 q^{93} +(-333358. - 242199. i) q^{94} +(-7.06669e6 - 9.79992e6i) q^{95} +(3.47371e6 - 2.52380e6i) q^{96} +(6.70521e6 - 4.87162e6i) q^{97} +(486526. + 1.49737e6i) q^{98} +1.99444e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9}+O(q^{10}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16} + 71504 q^{17} + 116208 q^{18} - 48685 q^{19} - 138265 q^{20} - 2274 q^{21} - 271952 q^{22} - 63227 q^{23} + 553980 q^{24} + 276615 q^{25} + 675246 q^{26} - 270235 q^{27} - 782613 q^{28} - 99655 q^{29} - 1011285 q^{30} + 39051 q^{31} + 1045974 q^{32} + 1766456 q^{33} + 605893 q^{34} - 476935 q^{35} - 2928227 q^{36} + 83909 q^{37} + 1937525 q^{38} + 1316257 q^{39} + 2903410 q^{40} - 1964944 q^{41} - 3462547 q^{42} - 3439822 q^{43} - 3557652 q^{44} - 2121790 q^{45} + 2982521 q^{46} + 1663474 q^{47} + 1678378 q^{48} + 6584354 q^{49} + 408485 q^{50} + 3922076 q^{51} - 5301176 q^{52} + 788553 q^{53} - 6946145 q^{54} - 2630560 q^{55} - 415350 q^{56} - 14598410 q^{57} + 4727030 q^{58} - 3625740 q^{59} + 29158890 q^{60} - 4161559 q^{61} + 19658928 q^{62} + 2426738 q^{63} - 4408596 q^{64} - 2030220 q^{65} - 6985528 q^{66} + 8470434 q^{67} - 29099218 q^{68} - 360673 q^{69} - 22417320 q^{70} - 4808044 q^{71} + 25676065 q^{72} + 5517633 q^{73} + 14050068 q^{74} + 257240 q^{75} + 22502000 q^{76} - 9936772 q^{77} + 14948561 q^{78} - 5343505 q^{79} - 3987180 q^{80} - 5865817 q^{81} - 76614542 q^{82} - 645927 q^{83} + 5992628 q^{84} + 48268560 q^{85} - 27540609 q^{86} + 65370380 q^{87} - 3612320 q^{88} + 11153500 q^{89} + 7267975 q^{90} - 9123484 q^{91} - 33863736 q^{92} - 118704764 q^{93} - 30761227 q^{94} - 26382485 q^{95} + 1256206 q^{96} + 55538244 q^{97} + 102201752 q^{98} + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.341871	+	1.05217i	0.0302175	+	0.0929997i	0.965028	−	0.262148i	$-0.0844307\pi$
$2$	0.341871	+	1.05217i	0.0302175	+	0.0929997i	−0.934810	+	0.355147i	$0.884431\pi$
$3$	64.7040	−	47.0102i	1.38359	−	1.00523i	0.387052	−	0.922058i	$-0.373493\pi$
$3$	64.7040	−	47.0102i	1.38359	−	1.00523i	0.996535	−	0.0831768i	$-0.0265066\pi$
$4$	102.564	−	74.5171i	0.801281	−	0.582165i
$5$	265.518	+	87.3222i	0.949946	+	0.312413i
$5$	265.518	+	87.3222i	0.949946	+	0.312413i
$6$	71.5832	+	52.0083i	0.135295	+	0.0982976i
$7$	−1498.89			−1.65168			−0.825841	−	0.563903i	$-0.809299\pi$
$7$	−1498.89			−1.65168			−0.825841	+	0.563903i	$0.809299\pi$
$8$	228.032	+	165.675i	0.157464	+	0.114404i
$9$	1300.83	−	4003.53i	0.594799	−	1.83060i
$10$	−1.10492	+	309.224i	−0.000349405	+	0.0977851i
$11$	1464.09	+	4505.99i	0.331659	+	1.02074i	0.968344	+	0.249618i	$0.0803052\pi$
$11$	1464.09	+	4505.99i	0.331659	+	1.02074i	−0.636685	+	0.771124i	$0.719695\pi$
$12$	3133.23	−	9643.10i	0.523430	−	1.61095i
$13$	−1412.50	+	4347.23i	−0.178315	+	0.548796i	−0.999769	−	0.0214778i	$-0.993163\pi$
$13$	−1412.50	+	4347.23i	−0.178315	+	0.548796i	0.821455	+	0.570274i	$0.193163\pi$
$14$	−512.427	−	1577.09i	−0.0499096	−	0.153606i
$15$	21285.1	−	6831.96i	1.62838	−	0.522668i
$16$	4918.16	−	15136.5i	0.300181	−	0.923861i
$17$	8795.02	+	6389.96i	0.434176	+	0.315447i	0.783316	−	0.621623i	$-0.213526\pi$
$17$	8795.02	+	6389.96i	0.434176	+	0.315447i	−0.349141	+	0.937070i	$0.613526\pi$
$18$	4657.12			0.188219
$19$	−34970.7	−	25407.7i	−1.16968	−	0.849821i	−0.178708	−	0.983902i	$-0.557192\pi$
$19$	−34970.7	−	25407.7i	−1.16968	−	0.849821i	−0.990970	+	0.134081i	$0.957192\pi$
$20$	33739.6	−	10829.5i	0.943050	−	0.302694i
$21$	−96984.1	+	70463.1i	−2.28525	+	1.66033i
$22$	−4240.55	+	3080.94i	−0.0849069	+	0.0616885i
$23$	6401.66	+	19702.3i	0.109710	+	0.337652i	0.990807	−	0.135283i	$-0.0431945\pi$
$23$	6401.66	+	19702.3i	0.109710	+	0.337652i	−0.881097	+	0.472935i	$0.843195\pi$
$24$	22543.0			0.332869
$25$	62874.7	+	46371.2i	0.804796	+	0.593552i
$26$	−5056.93			−0.0564261
$27$	−49986.9	−	153844.i	−0.488746	−	1.50421i
$28$	−153732.	+	111693.i	−1.32346	+	0.961551i
$29$	−45559.9	+	33101.2i	−0.346888	+	0.252029i	−0.747562	−	0.664192i	$-0.768776\pi$
$29$	−45559.9	+	33101.2i	−0.346888	+	0.252029i	0.400674	+	0.916221i	$0.368776\pi$
$30$	14465.2	+	20059.9i	0.0978135	+	0.135645i
$31$	127561.	+	92678.3i	0.769044	+	0.558743i	0.901671	−	0.432423i	$-0.142341\pi$
$31$	127561.	+	92678.3i	0.769044	+	0.558743i	−0.132627	+	0.991166i	$0.542341\pi$
$32$	53686.2			0.289626
$33$	306560.	+	222729.i	1.48497	+	1.07889i
$34$	−3716.57	+	11438.4i	−0.0162168	+	0.0499103i
$35$	−397982.	−	130886.i	−1.56901	−	0.516007i
$36$	−164913.	−	507551.i	−0.589111	−	1.81310i
$37$	−82856.0	+	255005.i	−0.268917	+	0.827641i	0.721848	+	0.692051i	$0.243293\pi$
$37$	−82856.0	+	255005.i	−0.268917	+	0.827641i	−0.990765	+	0.135590i	$0.956707\pi$
$38$	14777.8	−	45481.3i	0.0436885	−	0.134459i
$39$	112970.	+	347685.i	0.304955	+	0.938555i
$40$	46079.6	+	63902.1i	0.113841	+	0.157872i
$41$	143028.	−	440194.i	0.324098	−	0.997472i	−0.647747	−	0.761855i	$-0.724289\pi$
$41$	143028.	−	440194.i	0.324098	−	0.997472i	0.971846	−	0.235617i	$-0.0757112\pi$
$42$	−107295.	−	77954.6i	−0.223464	−	0.162356i
$43$	−419904.			−0.805398			−0.402699	−	0.915332i	$-0.631928\pi$
$43$	−419904.			−0.805398			−0.402699	+	0.915332i	$0.631928\pi$
$44$	485936.	+	353053.i	0.859993	+	0.624821i
$45$	694989.	−	949418.i	1.13693	−	1.55315i
$46$	−18541.6	+	13471.3i	−0.0280864	+	0.0204059i
$47$	−301322.	+	218923.i	−0.423339	+	0.307573i	−0.778980	−	0.627049i	$-0.784263\pi$
$47$	−301322.	+	218923.i	−0.423339	+	0.307573i	0.355641	+	0.934623i	$0.384263\pi$
$48$	−393347.	−	1.21060e6i	−0.513371	−	1.57999i
$49$	1.42313e6			1.72805
$50$	−27295.5	+	82008.0i	−0.0308813	+	0.0927814i
$51$	869466.			0.917819
$52$	179071.	+	551125.i	0.176610	+	0.543548i
$53$	9133.30	−	6635.73i	0.00842679	−	0.00612242i	−0.583564	−	0.812067i	$-0.698342\pi$
$53$	9133.30	−	6635.73i	0.00842679	−	0.00612242i	0.591991	+	0.805945i	$0.298342\pi$
$54$	144781.	−	105190.i	0.125122	−	0.0909066i
$55$	−4731.88	+	1.32427e6i	−0.00383499	+	1.07327i
$56$	−341795.	−	248329.i	−0.260081	−	0.188960i
$57$	−3.45716e6			−2.47262
$58$	−50403.8	−	36620.5i	−0.0339207	−	0.0246448i
$59$	−561895.	+	1.72933e6i	−0.356183	+	1.09622i	0.599137	+	0.800646i	$0.295510\pi$
$59$	−561895.	+	1.72933e6i	−0.356183	+	1.09622i	−0.955320	+	0.295572i	$0.904490\pi$
$60$	1.67399e6	−	2.28682e6i	1.00051	−	1.36679i
$61$	−623763.	−	1.91975e6i	−0.351856	−	1.08290i	−0.957810	−	0.287402i	$-0.907208\pi$
$61$	−623763.	−	1.91975e6i	−0.351856	−	1.08290i	0.605954	−	0.795500i	$-0.292792\pi$
$62$	−53904.2	+	165900.i	−0.0287244	+	0.0884047i
$63$	−1.94979e6	+	6.00085e6i	−0.982419	+	3.02357i
$64$	−611171.	−	1.88099e6i	−0.291429	−	0.896926i
$65$	−754654.	+	1.03093e6i	−0.340840	+	0.465619i
$66$	−129545.	+	398698.i	−0.0554647	+	0.170703i
$67$	−206291.	−	149879.i	−0.0837952	−	0.0608808i	0.545099	−	0.838372i	$-0.316492\pi$
$67$	−206291.	−	149879.i	−0.0837952	−	0.0608808i	−0.628894	+	0.777491i	$0.716492\pi$
$68$	1.37821e6			0.531539
$69$	1.34042e6	+	973872.i	0.491212	+	0.356886i
$70$	1656.15	−	463492.i	0.000577106	−	0.161510i
$71$	261849.	−	190244.i	0.0868253	−	0.0630823i	−0.543526	−	0.839392i	$-0.682911\pi$
$71$	261849.	−	190244.i	0.0868253	−	0.0630823i	0.630351	+	0.776310i	$0.282911\pi$
$72$	959916.	−	697420.i	0.303089	−	0.220207i
$73$	1.22989e6	+	3.78520e6i	0.370028	+	1.13883i	0.946772	+	0.321904i	$0.104323\pi$
$73$	1.22989e6	+	3.78520e6i	0.370028	+	1.13883i	−0.576744	+	0.816925i	$0.695677\pi$
$74$	−296635.			−0.0850964
$75$	6.24816e6	+	44652.4i	1.71016	+	0.0122217i
$76$	−5.48004e6			−1.43198
$77$	−2.19450e6	−	6.75399e6i	−0.547796	−	1.68594i
$78$	−327203.	+	237727.i	−0.0780704	+	0.0567215i
$79$	3.44694e6	−	2.50434e6i	0.786572	−	0.571478i	−0.120372	−	0.992729i	$-0.538409\pi$
$79$	3.44694e6	−	2.50434e6i	0.786572	−	0.571478i	0.906944	+	0.421251i	$0.138409\pi$
$80$	2.62762e6	−	3.58956e6i	0.573782	−	0.783838i
$81$	−3.01853e6	−	2.19309e6i	−0.631100	−	0.458521i
$82$	512057.			0.102558
$83$	−3.43591e6	−	2.49633e6i	−0.659581	−	0.479214i	0.206940	−	0.978354i	$-0.433649\pi$
$83$	−3.43591e6	−	2.49633e6i	−0.659581	−	0.479214i	−0.866521	+	0.499140i	$0.833649\pi$
$84$	−4.69637e6	+	1.44539e7i	−0.864540	+	2.66078i
$85$	1.77725e6	+	2.46465e6i	0.313894	+	0.435300i
$86$	−143553.	−	441811.i	−0.0243371	−	0.0749018i
$87$	−1.39181e6	+	4.28356e6i	−0.226602	+	0.697408i
$88$	−412673.	+	1.27008e6i	−0.0645530	+	0.198674i
$89$	−3.63725e6	−	1.11943e7i	−0.546900	−	1.68318i	−0.716429	−	0.697660i	$-0.754225\pi$
$89$	−3.63725e6	−	1.11943e7i	−0.546900	−	1.68318i	0.169529	−	0.985525i	$-0.445775\pi$
$90$	1.23655e6	+	406669.i	0.178798	+	0.0588021i
$91$	2.11718e6	−	6.51602e6i	0.294519	−	0.906436i
$92$	2.12474e6	+	1.54371e6i	0.284477	+	0.206685i
$93$	1.26105e7			1.62571
$94$	−333358.	−	242199.i	−0.0413965	−	0.0300763i
$95$	−7.06669e6	−	9.79992e6i	−0.845636	−	1.17271i
$96$	3.47371e6	−	2.52380e6i	0.400723	−	0.291142i
$97$	6.70521e6	−	4.87162e6i	0.745953	−	0.541967i	−0.148617	−	0.988895i	$-0.547482\pi$
$97$	6.70521e6	−	4.87162e6i	0.745953	−	0.541967i	0.894570	+	0.446928i	$0.147482\pi$
$98$	486526.	+	1.49737e6i	0.0522174	+	0.160709i
$99$	1.99444e7			2.06584
$100$	9.90413e6	+	70779.7i	0.990413	+	0.00707797i
$101$	1.15803e7			1.11840			0.559198	−	0.829034i	$-0.311109\pi$
$101$	1.15803e7			1.11840			0.559198	+	0.829034i	$0.311109\pi$
$102$	297245.	+	914827.i	0.0277341	+	0.0853569i
$103$	−1.02840e7	+	7.47176e6i	−0.927324	+	0.673740i	−0.945336	−	0.326098i	$-0.894266\pi$
$103$	−1.02840e7	+	7.47176e6i	−0.927324	+	0.673740i	0.0180125	+	0.999838i	$0.494266\pi$
$104$	−1.04232e6	+	757293.i	−0.0908628	+	0.0660157i
$105$	−3.19040e7	+	1.02404e7i	−2.68957	+	0.863281i
$106$	10104.3	+	7341.23i	0.000824019	+	0.000598685i
$107$	−2.31361e7			−1.82578			−0.912888	−	0.408209i	$-0.866153\pi$
$107$	−2.31361e7			−1.82578			−0.912888	+	0.408209i	$0.866153\pi$
$108$	−1.65909e7	−	1.20540e7i	−1.26732	−	0.920761i
$109$	−2.33772e6	+	7.19477e6i	−0.172902	+	0.532138i	−0.999531	−	0.0306087i	$-0.990255\pi$
$109$	−2.33772e6	+	7.19477e6i	−0.172902	+	0.532138i	0.826629	+	0.562747i	$0.190255\pi$
$110$	−1.39498e6	+	447751.i	−0.0999293	+	0.0320747i
$111$	6.62670e6	+	2.03949e7i	0.459904	+	1.41544i
$112$	−7.37178e6	+	2.26880e7i	−0.495803	+	1.52593i
$113$	6.32143e6	−	1.94554e7i	0.412136	−	1.26843i	−0.502651	−	0.864489i	$-0.667642\pi$
$113$	6.32143e6	−	1.94554e7i	0.412136	−	1.26843i	0.914787	−	0.403936i	$-0.132358\pi$
$114$	−1.18190e6	−	3.63753e6i	−0.0747163	−	0.229953i
$115$	−20689.9	+	5.79031e6i	−0.00126858	+	0.355026i
$116$	−2.20620e6	+	6.78998e6i	−0.131233	+	0.403892i
$117$	1.55668e7	+	1.13100e7i	0.898566	+	0.652846i
$118$	−2.01165e6			−0.112711
$119$	−1.31828e7	−	9.57784e6i	−0.717121	−	0.521019i
$120$	5.98558e6	+	1.96851e6i	0.316207	+	0.103993i
$121$	−2.39498e6	+	1.74006e6i	−0.122900	+	0.0892924i
$122$	1.80666e6	−	1.31261e6i	0.0900774	−	0.0654451i
$123$	−1.14391e7	−	3.52061e7i	−0.554276	−	1.70588i
$124$	1.99893e7			0.941501
$125$	1.26451e7	+	1.78028e7i	0.579079	+	0.815271i
$126$	−6.98050e6			−0.310878
$127$	−1.89199e6	−	5.82295e6i	−0.0819608	−	0.252249i	0.901676	−	0.432412i	$-0.142337\pi$
$127$	−1.89199e6	−	5.82295e6i	−0.0819608	−	0.252249i	−0.983637	+	0.180163i	$0.942337\pi$
$128$	7.32961e6	−	5.32527e6i	0.308920	−	0.224444i
$129$	−2.71695e7	+	1.97398e7i	−1.11434	+	0.809614i
$130$	−1.34271e6	−	441582.i	−0.0536018	−	0.0176283i
$131$	−6.38702e6	−	4.64044e6i	−0.248227	−	0.180347i	0.456714	−	0.889614i	$-0.349026\pi$
$131$	−6.38702e6	−	4.64044e6i	−0.248227	−	0.180347i	−0.704941	+	0.709266i	$0.749026\pi$
$132$	4.80391e7			1.81797
$133$	5.24172e7	+	3.80833e7i	1.93194	+	1.40363i
$134$	87173.9	−	268294.i	0.00312982	−	0.00963260i
$135$	161556.	−	4.52133e7i	0.00565139	−	1.58161i
$136$	946892.	+	2.91424e6i	0.0322786	+	0.0993433i
$137$	6.25403e6	−	1.92479e7i	0.207796	−	0.639531i	−0.791791	−	0.610792i	$-0.790851\pi$
$137$	6.25403e6	−	1.92479e7i	0.207796	−	0.639531i	0.999587	−	0.0287386i	$-0.00914904\pi$
$138$	−566430.	+	1.74329e6i	−0.0183472	+	0.0564668i
$139$	−1.02211e7	−	3.14574e7i	−0.322810	−	0.993507i	−0.972419	−	0.233239i	$-0.925068\pi$
$139$	−1.02211e7	−	3.14574e7i	−0.322810	−	0.993507i	0.649610	−	0.760268i	$-0.274932\pi$
$140$	−5.05719e7	+	1.62323e7i	−1.55762	+	0.499955i
$141$	−9.20509e6	+	2.83304e7i	−0.276542	+	0.851109i
$142$	289688.	+	210471.i	0.00849027	+	0.00616854i
$143$	−2.16566e7			−0.619319
$144$	−5.42019e7	−	3.93800e7i	−1.51268	−	1.09902i
$145$	−1.49874e7	+	4.81058e6i	−0.408262	+	0.131042i
$146$	−3.56222e6	+	2.58810e6i	−0.0947295	+	0.0688250i
$147$	9.20819e7	−	6.69014e7i	2.39091	−	1.73710i
$148$	1.05042e7	+	3.23285e7i	0.266346	+	0.819727i
$149$	−1.22724e7			−0.303934			−0.151967	−	0.988386i	$-0.548561\pi$
$149$	−1.22724e7			−0.303934			−0.151967	+	0.988386i	$0.548561\pi$
$150$	2.08909e6	+	6.58940e6i	0.0505402	+	0.159414i
$151$	1.92646e7			0.455346			0.227673	−	0.973738i	$-0.426888\pi$
$151$	1.92646e7			0.455346			0.227673	+	0.973738i	$0.426888\pi$
$152$	−3.76503e6	−	1.15876e7i	−0.0869592	−	0.267633i
$153$	3.70232e7	−	2.68989e7i	0.835706	−	0.607176i
$154$	6.35612e6	−	4.61799e6i	0.140239	−	0.101890i
$155$	2.57768e7	+	3.57467e7i	0.555992	+	0.771036i
$156$	3.74951e7	+	2.72418e7i	0.790748	+	0.574512i
$157$	−7.93594e7			−1.63663			−0.818314	−	0.574772i	$-0.805091\pi$
$157$	−7.93594e7			−1.63663			−0.818314	+	0.574772i	$0.805091\pi$
$158$	3.81341e6	+	2.77060e6i	0.0769155	+	0.0558824i
$159$	279014.	−	858716.i	0.00550472	−	0.0169418i
$160$	1.42546e7	+	4.68799e6i	0.275129	+	0.0904830i
$161$	−9.59537e6	−	2.95315e7i	−0.181205	−	0.557693i
$162$	1.27556e6	−	3.92577e6i	0.0235721	−	0.0725474i
$163$	1.41670e7	−	4.36014e7i	0.256224	−	0.788576i	−0.737362	−	0.675498i	$-0.763929\pi$
$163$	1.41670e7	−	4.36014e7i	0.256224	−	0.788576i	0.993586	−	0.113079i	$-0.0360712\pi$
$164$	−1.81325e7	−	5.58061e7i	−0.320999	−	0.987935i
$165$	6.19480e7	+	8.59080e7i	1.07358	+	1.48881i
$166$	1.45193e6	−	4.46859e6i	0.0246359	−	0.0758215i
$167$	2.40315e7	+	1.74599e7i	0.399277	+	0.290092i	0.769246	−	0.638952i	$-0.220632\pi$
$167$	2.40315e7	+	1.74599e7i	0.399277	+	0.290092i	−0.369970	+	0.929044i	$0.620632\pi$
$168$	−3.37895e7			−0.549793
$169$	3.38614e7	+	2.46017e7i	0.539636	+	0.392069i
$170$	−1.98564e6	+	2.71257e6i	−0.0309977	+	0.0423457i
$171$	−1.47211e8	+	1.06955e8i	−2.25141	+	1.63574i
$172$	−4.30670e7	+	3.12900e7i	−0.645350	+	0.468874i
$173$	4.43798e6	+	1.36587e7i	0.0651664	+	0.200562i	0.978338	−	0.207014i	$-0.0663744\pi$
$173$	4.43798e6	+	1.36587e7i	0.0651664	+	0.200562i	−0.913172	+	0.407575i	$0.866374\pi$
$174$	−4.98286e6			−0.0717061
$175$	−9.42422e7	−	6.95053e7i	−1.32927	−	0.980359i
$176$	7.54058e7			1.04258
$177$	4.49395e7	+	1.38310e8i	0.609147	+	1.87476i
$178$	1.05349e7	−	7.65402e6i	0.140010	−	0.101723i
$179$	−2.27557e6	+	1.65330e6i	−0.0296554	+	0.0215459i	−0.602514	−	0.798108i	$-0.705834\pi$
$179$	−2.27557e6	+	1.65330e6i	−0.0296554	+	0.0215459i	0.572859	+	0.819654i	$0.305834\pi$
$180$	532995.	−	1.49165e8i	0.00681191	−	1.90639i
$181$	7.36185e6	+	5.34870e6i	0.0922809	+	0.0670460i	0.632969	−	0.774177i	$-0.281836\pi$
$181$	7.36185e6	+	5.34870e6i	0.0922809	+	0.0670460i	−0.540688	+	0.841223i	$0.681836\pi$
$182$	7.57978e6			0.0931980
$183$	−1.30607e8	−	9.48919e7i	−1.57539	−	1.14459i
$184$	−1.80439e6	+	5.55335e6i	−0.0213535	+	0.0657193i
$185$	−4.42673e7	+	6.04732e7i	−0.514023	+	0.702201i
$186$	4.31117e6	+	1.32684e7i	0.0491247	+	0.151190i
$187$	−1.59164e7	+	4.89858e7i	−0.177992	+	0.547803i
$188$	−1.45912e7	+	4.49072e7i	−0.160155	+	0.492906i
$189$	7.49249e7	+	2.30595e8i	0.807253	+	2.48447i
$190$	7.89530e6	−	1.07857e7i	0.0835085	−	0.114080i
$191$	4.86946e7	−	1.49867e8i	0.505666	−	1.55628i	−0.293981	−	0.955811i	$-0.594980\pi$
$191$	4.86946e7	−	1.49867e8i	0.505666	−	1.55628i	0.799647	−	0.600470i	$-0.205020\pi$
$192$	−1.27971e8	−	9.29763e7i	−1.30484	−	0.948021i
$193$	−1.06836e7			−0.106972			−0.0534858	−	0.998569i	$-0.517033\pi$
$193$	−1.06836e7			−0.106972			−0.0534858	+	0.998569i	$0.517033\pi$
$194$	7.41811e6	+	5.38957e6i	0.0729436	+	0.0529966i
$195$	−365114.	+	1.02181e8i	−0.00352620	+	0.986849i
$196$	1.45962e8	−	1.06047e8i	1.38466	−	1.00601i
$197$	−3.85115e7	+	2.79803e7i	−0.358888	+	0.260747i	−0.752588	−	0.658492i	$-0.771195\pi$
$197$	−3.85115e7	+	2.79803e7i	−0.358888	+	0.260747i	0.393700	+	0.919239i	$0.371195\pi$
$198$	6.81842e6	+	2.09849e7i	0.0624246	+	0.192123i
$199$	−2.32663e7			−0.209287			−0.104643	−	0.994510i	$-0.533370\pi$
$199$	−2.32663e7			−0.209287			−0.104643	+	0.994510i	$0.533370\pi$
$200$	6.65490e6	+	2.09909e7i	0.0588216	+	0.185535i
$201$	−2.03937e7			−0.177137
$202$	3.95898e6	+	1.21845e7i	0.0337951	+	0.104011i
$203$	6.82892e7	−	4.96150e7i	0.572949	−	0.416272i
$204$	8.91759e7	−	6.47901e7i	0.735431	−	0.534322i
$205$	7.64152e7	−	1.04390e8i	0.619500	−	0.846293i
$206$	−1.13774e7	−	8.26615e6i	−0.0906790	−	0.0658822i
$207$	8.72060e7			0.683361
$208$	5.88551e7	+	4.27608e7i	0.453485	+	0.329476i
$209$	6.32868e7	−	1.94777e8i	0.479514	−	1.47579i
$210$	−2.16817e7	−	3.00676e7i	−0.161557	−	0.224043i
$211$	−7.77349e6	−	2.39243e7i	−0.0569675	−	0.175328i	0.918524	−	0.395365i	$-0.129382\pi$
$211$	−7.77349e6	−	2.39243e7i	−0.0569675	−	0.175328i	−0.975491	+	0.220037i	$0.929382\pi$
$212$	442272.	−	1.36117e6i	0.00318797	−	0.00981156i
$213$	7.99923e6	−	2.46191e7i	0.0567178	−	0.174560i
$214$	−7.90959e6	−	2.43432e7i	−0.0551703	−	0.169797i
$215$	−1.11492e8	−	3.66669e7i	−0.765085	−	0.251617i
$216$	1.40895e7	−	4.33630e7i	0.0951278	−	0.292773i
$217$	−1.91199e8	−	1.38915e8i	−1.27022	−	0.922866i
$218$	−8.36934e6			−0.0547134
$219$	2.57521e8	+	1.87100e8i	1.65676	+	1.20370i
$220$	9.81954e7	+	1.36175e8i	0.621744	+	0.862220i
$221$	−4.02016e7	+	2.92082e7i	−0.250536	+	0.182025i
$222$	−1.91935e7	+	1.39449e7i	−0.117738	+	0.0855419i
$223$	5.49517e7	+	1.69124e8i	0.331829	+	1.02126i	0.968263	+	0.249933i	$0.0804086\pi$
$223$	5.49517e7	+	1.69124e8i	0.331829	+	1.02126i	−0.636434	+	0.771331i	$0.719591\pi$
$224$	−8.04696e7			−0.478370
$225$	2.67437e8	−	1.91400e8i	1.56525	−	1.12022i
$226$	2.26315e7			0.130417
$227$	−1.56631e7	−	4.82062e7i	−0.0888768	−	0.273535i	0.896733	−	0.442572i	$-0.145934\pi$
$227$	−1.56631e7	−	4.82062e7i	−0.0888768	−	0.273535i	−0.985610	+	0.169038i	$0.945934\pi$
$228$	−3.54580e8	+	2.57618e8i	−1.98127	+	1.43947i
$229$	−1.23707e8	+	8.98783e7i	−0.680722	+	0.494573i	−0.873597	−	0.486650i	$-0.838219\pi$
$229$	−1.23707e8	+	8.98783e7i	−0.680722	+	0.494573i	0.192875	+	0.981223i	$0.438219\pi$
$230$	−6.09948e6	+	1.95777e6i	−0.0330556	+	0.0106100i
$231$	−4.59499e8	−	3.33846e8i	−2.45269	−	1.78198i
$232$	−1.58732e7			−0.0834557
$233$	2.10455e8	+	1.52905e8i	1.08997	+	0.791909i	0.979394	−	0.201959i	$-0.0647307\pi$
$233$	2.10455e8	+	1.52905e8i	1.08997	+	0.791909i	0.110575	+	0.993868i	$0.464731\pi$
$234$	−6.57818e6	+	2.02456e7i	−0.0335622	+	0.103294i
$235$	−9.91232e7	+	3.18159e7i	−0.498239	+	0.159922i
$236$	7.12348e7	+	2.19238e8i	0.352777	+	1.08574i
$237$	1.05301e8	−	3.24082e8i	0.513821	−	1.58138i
$238$	5.57072e6	−	1.71449e7i	0.0267850	−	0.0824359i
$239$	9.85051e7	+	3.03168e8i	0.466730	+	1.43645i	0.856793	+	0.515660i	$0.172453\pi$
$239$	9.85051e7	+	3.03168e8i	0.466730	+	1.43645i	−0.390063	+	0.920788i	$0.627547\pi$
$240$	1.27128e6	−	3.55784e8i	0.00593613	−	1.66129i
$241$	−6.97137e6	+	2.14557e7i	−0.0320818	+	0.0987375i	−0.965815	−	0.259232i	$-0.916531\pi$
$241$	−6.97137e6	+	2.14557e7i	−0.0320818	+	0.0987375i	0.933733	+	0.357969i	$0.116531\pi$
$242$	−2.64961e6	−	1.92506e6i	−0.0120179	−	0.00873152i
$243$	5.53633e7			0.247514
$244$	−2.07029e8	−	1.50416e8i	−0.912363	−	0.662871i
$245$	3.77866e8	+	1.24271e8i	1.64156	+	0.539867i
$246$	3.31321e7	−	2.40719e7i	0.141898	−	0.103095i
$247$	1.59849e8	−	1.16137e8i	0.674949	−	0.490379i
$248$	1.37335e7	+	4.22673e7i	0.0571742	+	0.175964i
$249$	−3.39670e8			−1.39431
$250$	−1.44086e7	+	1.93911e7i	−0.0583217	+	0.0784897i
$251$	−5.09920e7			−0.203537			−0.101769	−	0.994808i	$-0.532450\pi$
$251$	−5.09920e7			−0.203537			−0.101769	+	0.994808i	$0.532450\pi$
$252$	2.47187e8	+	7.60764e8i	0.973025	+	2.99466i
$253$	−7.94057e7	+	5.76916e7i	−0.308269	+	0.223971i
$254$	5.47993e6	−	3.98140e6i	0.0209825	−	0.0152447i
$255$	2.30859e8	+	7.59236e7i	0.871878	+	0.286739i
$256$	−1.96700e8	−	1.42911e8i	−0.732763	−	0.532383i
$257$	−4.08822e8			−1.50234			−0.751169	−	0.660110i	$-0.770510\pi$
$257$	−4.08822e8			−1.50234			−0.751169	+	0.660110i	$0.770510\pi$
$258$	−3.00581e7	−	2.18385e7i	−0.108966	−	0.0791687i
$259$	1.24192e8	−	3.82224e8i	0.444165	−	1.36700i
$260$	−578752.	+	1.61970e8i	−0.00204214	+	0.571517i
$261$	7.32561e7	+	2.25459e8i	0.255036	+	0.784921i
$262$	2.69900e6	−	8.30668e6i	0.00927148	−	0.0285347i
$263$	−9.24221e7	+	2.84446e8i	−0.313279	+	0.964172i	0.663179	+	0.748461i	$0.269207\pi$
$263$	−9.24221e7	+	2.84446e8i	−0.313279	+	0.964172i	−0.976457	+	0.215711i	$0.930793\pi$
$264$	3.30049e7	+	1.01579e8i	0.110399	+	0.339773i
$265$	3.00450e6	−	964366.i	0.00991772	−	0.00318333i
$266$	−2.21503e7	+	6.81715e7i	−0.0721594	+	0.222084i
$267$	−7.61590e8	−	5.53328e8i	−2.44868	−	1.77907i
$268$	−3.23266e7			−0.102586
$269$	2.69662e8	+	1.95921e8i	0.844670	+	0.613689i	0.923671	−	0.383186i	$-0.125173\pi$
$269$	2.69662e8	+	1.95921e8i	0.844670	+	0.613689i	−0.0790013	+	0.996875i	$0.525173\pi$
$270$	4.76274e7	−	1.52872e7i	0.147260	−	0.0472665i
$271$	−8.21719e7	+	5.97014e7i	−0.250802	+	0.182218i	−0.706082	−	0.708130i	$-0.749539\pi$
$271$	−8.21719e7	+	5.97014e7i	−0.250802	+	0.182218i	0.455280	+	0.890348i	$0.349539\pi$
$272$	1.39977e8	−	1.01699e8i	0.421761	−	0.306427i
$273$	−1.69329e8	−	5.21141e8i	−0.503689	−	1.55019i
$274$	2.23902e7			0.0657553
$275$	−1.16895e8	+	3.51204e8i	−0.338945	+	1.01835i
$276$	2.10049e8			0.601366
$277$	3.53914e7	+	1.08924e8i	0.100050	+	0.307924i	0.988537	−	0.150979i	$-0.0482426\pi$
$277$	3.53914e7	+	1.08924e8i	0.100050	+	0.307924i	−0.888487	+	0.458903i	$0.848243\pi$
$278$	2.96043e7	−	2.15088e7i	0.0826414	−	0.0600425i
$279$	5.36974e8	−	3.90135e8i	1.48026	−	1.07547i
$280$	−6.90682e7	−	9.57821e7i	−0.188029	−	0.260754i
$281$	5.34586e8	+	3.88399e8i	1.43729	+	1.04425i	0.988599	+	0.150569i	$0.0481107\pi$
$281$	5.34586e8	+	3.88399e8i	1.43729	+	1.04425i	0.448694	+	0.893685i	$0.351889\pi$
$282$	−3.29554e7			−0.0875093
$283$	−2.13097e8	−	1.54824e8i	−0.558887	−	0.406055i	0.272164	−	0.962251i	$-0.412261\pi$
$283$	−2.13097e8	−	1.54824e8i	−0.558887	−	0.406055i	−0.831051	+	0.556196i	$0.812261\pi$
$284$	1.26798e7	−	3.90244e7i	0.0328472	−	0.101093i
$285$	−9.17939e8	−	3.01887e8i	−2.34886	−	0.772480i
$286$	−7.40378e6	−	2.27865e7i	−0.0187142	−	0.0575965i
$287$	−2.14383e8	+	6.59803e8i	−0.535308	+	1.64751i
$288$	6.98363e7	−	2.14934e8i	0.172269	−	0.530190i
$289$	−9.02808e7	−	2.77856e8i	−0.220015	−	0.677137i
$290$	−1.01853e7	−	1.41248e7i	−0.0245235	−	0.0340086i
$291$	2.04838e8	−	6.30426e8i	0.487287	−	1.49972i
$292$	4.08204e8	+	2.96578e8i	0.959483	+	0.697105i
$293$	6.58281e8			1.52888			0.764442	−	0.644693i	$-0.223015\pi$
$293$	6.58281e8			1.52888			0.764442	+	0.644693i	$0.223015\pi$
$294$	1.01872e8	+	7.40143e7i	0.233797	+	0.169864i
$295$	−3.00203e8	+	4.10104e8i	−0.680828	+	0.930072i
$296$	−6.11418e7	+	4.44221e7i	−0.137031	+	0.0995586i
$297$	6.20035e8	−	4.50482e8i	1.37331	−	0.997768i
$298$	−4.19560e6	−	1.29127e7i	−0.00918410	−	0.0282658i
$299$	−9.46926e7			−0.204865
$300$	6.44164e8	−	4.61015e8i	1.37744	−	0.985804i
$301$	6.29390e8			1.33026
$302$	6.58603e6	+	2.02697e7i	0.0137594	+	0.0423471i
$303$	7.49292e8	−	5.44392e8i	1.54740	−	1.12425i
$304$	−5.56576e8	+	4.04376e8i	−1.13623	+	0.825521i
$305$	2.01598e6	−	5.64195e8i	0.00406852	−	1.13862i
$306$	4.09594e7	+	2.97588e7i	0.0817201	+	0.0593731i
$307$	7.67111e8			1.51312			0.756561	−	0.653923i	$-0.226878\pi$
$307$	7.67111e8			1.51312			0.756561	+	0.653923i	$0.226878\pi$
$308$	−7.28365e8	−	5.29188e8i	−1.42043	−	1.03201i
$309$	−3.14166e8	+	9.66904e8i	−0.605766	+	1.86436i
$310$	−2.87993e7	+	3.93424e7i	−0.0549055	+	0.0750058i
$311$	−2.31405e8	−	7.12191e8i	−0.436226	−	1.34257i	−0.891825	−	0.452380i	$-0.850575\pi$
$311$	−2.31405e8	−	7.12191e8i	−0.436226	−	1.34257i	0.455599	−	0.890185i	$-0.349425\pi$
$312$	−3.18420e7	+	9.79997e7i	−0.0593553	+	0.182677i
$313$	−1.08509e8	+	3.33957e8i	−0.200014	+	0.615581i	0.799867	+	0.600177i	$0.204903\pi$
$313$	−1.08509e8	+	3.33957e8i	−0.200014	+	0.615581i	−0.999881	+	0.0154036i	$0.995097\pi$
$314$	−2.71307e7	−	8.34998e7i	−0.0494547	−	0.152206i
$315$	−1.04171e9	+	1.42307e9i	−1.87785	+	2.56531i
$316$	1.66915e8	−	5.13711e8i	0.297571	−	0.915829i
$317$	−4.38989e6	−	3.18944e6i	−0.00774009	−	0.00562351i	0.583908	−	0.811819i	$-0.301523\pi$
$317$	−4.38989e6	−	3.18944e6i	−0.00774009	−	0.00562351i	−0.591649	+	0.806196i	$0.701523\pi$
$318$	998904.			0.00174192
$319$	−2.15857e8	−	1.56830e8i	−0.372306	−	0.270496i
$320$	1.97528e6	−	5.52806e8i	0.00336980	−	0.943078i
$321$	−1.49700e9	+	1.08763e9i	−2.52612	+	1.83533i
$322$	2.77919e7	−	2.01920e7i	0.0463898	−	0.0337041i
$323$	−1.45214e8	−	4.46922e8i	−0.239772	−	0.737944i
$324$	−4.73015e8			−0.772623
$325$	−2.90397e8	+	2.07831e8i	−0.469246	+	0.335830i
$326$	5.07194e7			0.0810798
$327$	1.86968e8	+	5.75427e8i	0.295699	+	0.910067i
$328$	1.05544e8	−	7.66824e7i	0.165149	−	0.119988i
$329$	4.51648e8	−	3.28141e8i	0.699221	−	0.508014i
$330$	−6.92117e7	+	9.45494e7i	−0.106018	+	0.144831i
$331$	1.20150e8	+	8.72944e7i	0.182107	+	0.132309i	0.675104	−	0.737722i	$-0.264099\pi$
$331$	1.20150e8	+	8.72944e7i	0.182107	+	0.132309i	−0.492997	+	0.870031i	$0.664099\pi$
$332$	−5.38420e8			−0.807491
$333$	9.13137e8	+	6.63433e8i	1.35513	+	0.984560i
$334$	−1.01552e7	+	3.12544e7i	−0.0149133	+	0.0458985i
$335$	−4.16863e7	−	5.78095e7i	−0.0605810	−	0.0840122i
$336$	5.89584e8	+	1.81455e9i	0.847926	+	2.60965i
$337$	1.95656e8	−	6.02168e8i	0.278477	−	0.857064i	−0.709802	−	0.704402i	$-0.751215\pi$
$337$	1.95656e8	−	6.02168e8i	0.278477	−	0.857064i	0.988278	−	0.152662i	$-0.0487846\pi$
$338$	−1.43090e7	+	4.40386e7i	−0.0201559	+	0.0620333i
$339$	−5.05578e8	−	1.55601e9i	−0.704839	−	2.16927i
$340$	3.65941e8	+	1.20349e8i	0.504934	+	0.166060i
$341$	−2.30848e8	+	7.10477e8i	−0.315272	+	0.970308i
$342$	−1.62862e8	−	1.18327e8i	−0.220156	−	0.159952i
$343$	−8.98710e8			−1.20251
$344$	−9.57518e7	−	6.95677e7i	−0.126821	−	0.0921411i
$345$	2.70865e8	+	3.75629e8i	0.355129	+	0.492484i
$346$	−1.28541e7	+	9.33903e6i	−0.0166830	+	0.0121209i
$347$	1.19343e9	−	8.67074e8i	1.53335	−	1.11405i	0.579015	−	0.815317i	$-0.303437\pi$
$347$	1.19343e9	−	8.67074e8i	1.53335	−	1.11405i	0.954338	−	0.298730i	$-0.0965629\pi$
$348$	1.76448e8	+	5.43052e8i	0.224435	+	0.690740i
$349$	8.19578e8			1.03205			0.516026	−	0.856573i	$-0.327411\pi$
$349$	8.19578e8			1.03205			0.516026	+	0.856573i	$0.327411\pi$
$350$	4.09129e7	−	1.22921e8i	0.0510061	−	0.153245i
$351$	7.39402e8			0.912653
$352$	7.86012e7	+	2.41910e8i	0.0960572	+	0.295634i
$353$	1.84028e8	−	1.33704e8i	0.222676	−	0.161784i	−0.470854	−	0.882211i	$-0.656054\pi$
$353$	1.84028e8	−	1.33704e8i	0.222676	−	0.161784i	0.693530	+	0.720427i	$0.256054\pi$
$354$	−1.30162e8	+	9.45682e7i	−0.155945	+	0.113301i
$355$	8.61381e7	−	2.76481e7i	0.102187	−	0.0327994i
$356$	−1.20722e9	−	8.77095e8i	−1.41811	−	1.03032i
$357$	−1.30323e9			−1.51594
$358$	−2.51750e6	−	1.82907e6i	−0.00289988	−	0.00210688i
$359$	−8.20397e7	+	2.52492e8i	−0.0935823	+	0.288017i	−0.986882	−	0.161446i	$-0.948384\pi$
$359$	−8.20397e7	+	2.52492e8i	−0.0935823	+	0.288017i	0.893299	+	0.449462i	$0.148384\pi$
$360$	3.15775e8	−	1.01356e8i	0.356713	−	0.114496i
$361$	3.01177e8	+	9.26926e8i	0.336935	+	1.03698i
$362$	−3.11094e6	+	9.57450e6i	−0.00344677	+	0.0106081i
$363$	−7.31645e7	+	2.25177e8i	−0.0802836	+	0.247088i
$364$	−2.68408e8	−	8.26075e8i	−0.291703	−	0.897769i
$365$	−3.97495e6	+	1.11243e9i	−0.00427865	+	1.19743i
$366$	5.51916e7	−	1.69862e8i	0.0588423	−	0.181098i
$367$	5.76380e7	+	4.18765e7i	0.0608664	+	0.0442220i	0.617802	−	0.786333i	$-0.288023\pi$
$367$	5.76380e7	+	4.18765e7i	0.0608664	+	0.0442220i	−0.556936	+	0.830555i	$0.688023\pi$
$368$	3.29709e8			0.344876
$369$	−1.57628e9	−	1.14523e9i	−1.63320	−	1.18659i
$370$	−7.87619e7	−	2.59028e7i	−0.0808370	−	0.0265853i
$371$	−1.36898e7	+	9.94622e6i	−0.0139184	+	0.0101123i
$372$	1.29338e9	−	9.39699e8i	1.30265	−	0.946430i
$373$	−1.03736e8	−	3.19266e8i	−0.103502	−	0.318545i	0.885874	−	0.463925i	$-0.153559\pi$
$373$	−1.03736e8	−	3.19266e8i	−0.103502	−	0.318545i	−0.989376	+	0.145380i	$0.953559\pi$
$374$	−5.69828e7			−0.0563240
$375$	1.65510e9	+	5.57459e8i	1.62075	+	0.545888i
$376$	−1.04981e8			−0.101848
$377$	−7.95451e7	−	2.44815e8i	−0.0764573	−	0.235311i
$378$	−2.17011e8	+	1.57668e8i	−0.206662	+	0.150149i
$379$	−1.54931e9	+	1.12564e9i	−1.46185	+	1.06209i	−0.478970	+	0.877831i	$0.658990\pi$
$379$	−1.54931e9	+	1.12564e9i	−1.46185	+	1.06209i	−0.982877	+	0.184263i	$0.941010\pi$
$380$	−1.45505e9	−	4.78529e8i	−1.36030	−	0.447369i
$381$	−3.96157e8	−	2.87825e8i	−0.366970	−	0.266619i
$382$	1.74333e8			0.160014
$383$	7.25747e7	+	5.27286e7i	0.0660069	+	0.0479568i	0.620299	−	0.784365i	$-0.287011\pi$
$383$	7.25747e7	+	5.27286e7i	0.0660069	+	0.0479568i	−0.554293	+	0.832322i	$0.687011\pi$
$384$	2.23913e8	−	6.89133e8i	0.201799	−	0.621074i
$385$	7.09256e6	−	1.98493e9i	0.00633418	−	1.77269i
$386$	−3.65243e6	−	1.12410e7i	−0.00323241	−	0.00994832i
$387$	−5.46222e8	+	1.68110e9i	−0.479050	+	1.47436i
$388$	3.24694e8	−	9.99306e8i	0.282204	−	0.868535i
$389$	5.81896e8	+	1.79089e9i	0.501212	+	1.54257i	0.807047	+	0.590487i	$0.201064\pi$
$389$	5.81896e8	+	1.79089e9i	0.501212	+	1.54257i	−0.305835	+	0.952085i	$0.598936\pi$
$390$	−1.07637e8	+	3.45487e7i	−0.0918832	+	0.0294921i
$391$	−6.95940e7	+	2.14188e8i	−0.0588780	+	0.181208i
$392$	3.24519e8	+	2.35777e8i	0.272107	+	0.197697i
$393$	−6.31414e8			−0.524735
$394$	−4.26060e7	−	3.09551e7i	−0.0350941	−	0.0254974i
$395$	1.13391e9	−	3.63955e8i	0.925738	−	0.297138i
$396$	2.04558e9	−	1.48620e9i	1.65532	−	1.20266i
$397$	7.47837e8	−	5.43335e8i	0.599846	−	0.435814i	−0.245978	−	0.969275i	$-0.579109\pi$
$397$	7.47837e8	−	5.43335e8i	0.599846	−	0.435814i	0.845824	+	0.533461i	$0.179109\pi$
$398$	−7.95409e6	−	2.44802e7i	−0.00632411	−	0.0194636i
$399$	5.18190e9			4.08399
$400$	1.01113e9	−	7.23644e8i	0.789944	−	0.565347i
$401$	−9.36336e8			−0.725148			−0.362574	−	0.931955i	$-0.618102\pi$
$401$	−9.36336e8			−0.725148			−0.362574	+	0.931955i	$0.618102\pi$
$402$	−6.97203e6	−	2.14577e7i	−0.00535264	−	0.0164737i
$403$	−5.83074e8	+	4.23628e8i	−0.443768	+	0.322416i
$404$	1.18772e9	−	8.62931e8i	0.896149	−	0.651091i
$405$	−6.09969e8	−	8.45890e8i	−0.456263	−	0.632734i
$406$	7.55497e7	+	5.48901e7i	0.0560262	+	0.0407054i
$407$	−1.27036e9			−0.933997
$408$	1.98266e8	+	1.44049e8i	0.144524	+	0.105002i
$409$	−7.92098e8	+	2.43783e9i	−0.572463	+	1.76186i	0.0721974	+	0.997390i	$0.476999\pi$
$409$	−7.92098e8	+	2.43783e9i	−0.572463	+	1.76186i	−0.644660	+	0.764469i	$0.723001\pi$
$410$	1.35960e8	+	4.47140e7i	0.0974247	+	0.0320405i
$411$	−5.00188e8	−	1.53942e9i	−0.355375	−	1.09373i
$412$	−4.97993e8	+	1.53267e9i	−0.350819	+	1.07971i
$413$	8.42218e8	−	2.59208e9i	0.588301	−	1.81060i
$414$	2.98132e7	+	9.17557e7i	0.0206494	+	0.0635524i
$415$	−6.94310e8	−	9.62852e8i	−0.476854	−	0.661289i
$416$	−7.58318e7	+	2.33386e8i	−0.0516445	+	0.158946i
$417$	−2.14016e9	−	1.55492e9i	−1.44534	−	1.05010i
$418$	2.26575e8			0.151738
$419$	−3.21278e8	−	2.33422e8i	−0.213370	−	0.155022i	0.475967	−	0.879463i	$-0.342098\pi$
$419$	−3.21278e8	−	2.33422e8i	−0.213370	−	0.155022i	−0.689337	+	0.724441i	$0.742098\pi$
$420$	−2.50912e9	+	3.42769e9i	−1.65253	+	2.25750i
$421$	1.16250e8	−	8.44602e7i	0.0759283	−	0.0551652i	−0.549174	−	0.835708i	$-0.685057\pi$
$421$	1.16250e8	−	8.44602e7i	0.0759283	−	0.0551652i	0.625102	+	0.780543i	$0.285057\pi$
$422$	2.25150e7	−	1.63581e7i	0.0145840	−	0.0105959i
$423$	4.84498e8	+	1.49113e9i	0.311243	+	0.957909i
$424$	3.18206e6			0.00202735
$425$	2.56674e8	+	8.09602e8i	0.162189	+	0.511576i
$426$	2.86382e7			0.0179479
$427$	9.34952e8	+	2.87749e9i	0.581155	+	1.78861i
$428$	−2.37293e9	+	1.72404e9i	−1.46296	+	1.06290i
$429$	−1.40127e9	+	1.01808e9i	−0.856882	+	0.622561i
$430$	463959.	−	1.29844e8i	0.000281410	−	0.0787559i
$431$	−5.84315e8	−	4.24530e8i	−0.351542	−	0.255410i	0.397974	−	0.917397i	$-0.369713\pi$
$431$	−5.84315e8	−	4.24530e8i	−0.351542	−	0.255410i	−0.749515	+	0.661987i	$0.769713\pi$
$432$	−2.57451e9			−1.53639
$433$	7.84617e8	+	5.70058e8i	0.464462	+	0.337451i	0.795279	−	0.606244i	$-0.207324\pi$
$433$	7.84617e8	+	5.70058e8i	0.464462	+	0.337451i	−0.330817	+	0.943695i	$0.607324\pi$
$434$	8.07964e7	−	2.48666e8i	0.0474436	−	0.146016i
$435$	−7.43601e8	+	1.01583e9i	−0.433139	+	0.591707i
$436$	2.96367e8	+	9.12125e8i	0.171249	+	0.527050i
$437$	2.76719e8	−	8.51653e8i	0.158618	−	0.488177i
$438$	−1.08822e8	+	3.34921e8i	−0.0618812	+	0.190451i
$439$	3.69708e8	+	1.13784e9i	0.208561	+	0.641884i	0.999548	+	0.0300519i	$0.00956727\pi$
$439$	3.69708e8	+	1.13784e9i	0.208561	+	0.641884i	−0.790988	+	0.611832i	$0.790433\pi$
$440$	−2.20478e8	+	3.01193e8i	−0.123390	+	0.168562i
$441$	1.85124e9	−	5.69753e9i	1.02784	−	3.16338i
$442$	−4.44758e7	−	3.23136e7i	−0.0244989	−	0.0177995i
$443$	−2.32438e9			−1.27026			−0.635132	−	0.772403i	$-0.719054\pi$
$443$	−2.32438e9			−1.27026			−0.635132	+	0.772403i	$0.719054\pi$
$444$	2.19943e9	+	1.59798e9i	1.19253	+	0.866424i
$445$	1.17555e7	−	3.28990e9i	0.00632382	−	1.76979i
$446$	−1.59161e8	+	1.15637e8i	−0.0849503	+	0.0617200i
$447$	−7.94075e8	+	5.76929e8i	−0.420519	+	0.305525i
$448$	9.16078e8	+	2.81940e9i	0.481348	+	1.48144i
$449$	−2.40068e9			−1.25162			−0.625810	−	0.779975i	$-0.715232\pi$
$449$	−2.40068e9			−1.25162			−0.625810	+	0.779975i	$0.715232\pi$
$450$	2.92815e8	+	2.15956e8i	0.151478	+	0.111718i
$451$	2.19292e9			1.12565
$452$	−8.01406e8	−	2.46647e9i	−0.408195	−	1.25630i
$453$	1.24650e9	−	9.05634e8i	0.630011	−	0.457730i
$454$	4.53664e7	−	3.29606e7i	0.0227530	−	0.0165310i
$455$	1.13114e9	−	1.54524e9i	0.562960	−	0.769054i
$456$	−7.88345e8	−	5.72766e8i	−0.389349	−	0.282879i
$457$	4.01224e8			0.196644			0.0983219	−	0.995155i	$-0.468653\pi$
$457$	4.01224e8			0.196644			0.0983219	+	0.995155i	$0.468653\pi$
$458$	−1.36859e8	−	9.94341e7i	−0.0665649	−	0.0483622i
$459$	5.43420e8	−	1.67248e9i	0.262296	−	0.807264i
$460$	4.29355e8	+	5.95420e8i	0.205667	+	0.285214i
$461$	4.26998e8	+	1.31417e9i	0.202989	+	0.624736i	0.999790	+	0.0204943i	$0.00652399\pi$
$461$	4.26998e8	+	1.31417e9i	0.202989	+	0.624736i	−0.796801	+	0.604242i	$0.793476\pi$
$462$	1.94173e8	−	5.97604e8i	0.0916100	−	0.281947i
$463$	−1.04970e9	+	3.23063e9i	−0.491507	+	1.51270i	0.330823	+	0.943693i	$0.392674\pi$
$463$	−1.04970e9	+	3.23063e9i	−0.491507	+	1.51270i	−0.822330	+	0.569010i	$0.807326\pi$
$464$	2.76967e8	+	8.52416e8i	0.128711	+	0.396131i
$465$	3.34832e9	+	1.10118e9i	1.54433	+	0.507893i
$466$	−8.89334e7	+	2.73709e8i	−0.0407112	+	0.125296i
$467$	2.04505e9	+	1.48581e9i	0.929167	+	0.675080i	0.945789	−	0.324782i	$-0.105291\pi$
$467$	2.04505e9	+	1.48581e9i	0.929167	+	0.675080i	−0.0166215	+	0.999862i	$0.505291\pi$
$468$	2.43938e9			1.10007
$469$	3.09208e8	+	2.24653e8i	0.138403	+	0.100556i
$470$	−6.73632e7	−	9.34177e7i	−0.0299282	−	0.0415037i
$471$	−5.13487e9	+	3.73070e9i	−2.26442	+	1.64519i
$472$	−4.14638e8	+	3.01252e8i	−0.181498	+	0.131866i
$473$	−6.14776e8	−	1.89209e9i	−0.267118	−	0.822104i
$474$	3.76989e8			0.162594
$475$	−1.02058e9	−	3.21913e9i	−0.436940	−	1.37820i
$476$	−2.06579e9			−0.877934
$477$	−1.46855e7	−	4.51973e7i	−0.00619547	−	0.0190677i
$478$	−2.85308e8	+	2.07289e8i	−0.119486	+	0.0868116i
$479$	2.71354e9	−	1.97151e9i	1.12814	−	0.819641i	0.142716	−	0.989764i	$-0.454416\pi$
$479$	2.71354e9	−	1.97151e9i	1.12814	−	0.819641i	0.985423	+	0.170123i	$0.0544164\pi$
$480$	1.14272e9	−	3.66782e8i	0.471622	−	0.151378i
$481$	−9.91530e8	−	7.20389e8i	−0.406254	−	0.295161i
$482$	−2.49584e7			−0.0101520
$483$	−2.00914e9	−	1.45973e9i	−0.811326	−	0.589463i
$484$	−1.15975e8	+	3.56934e8i	−0.0464949	+	0.143097i
$485$	2.20576e9	−	7.07990e8i	0.877933	−	0.281793i
$486$	1.89271e7	+	5.82517e7i	0.00747924	+	0.0230187i
$487$	2.49101e8	−	7.66654e8i	0.0977292	−	0.300780i	−0.890226	−	0.455519i	$-0.849454\pi$
$487$	2.49101e8	−	7.66654e8i	0.0977292	−	0.300780i	0.987955	+	0.154739i	$0.0494538\pi$
$488$	1.75816e8	−	5.41106e8i	0.0684840	−	0.210772i
$489$	−1.13305e9	−	3.48717e9i	−0.438196	−	1.34863i
$490$	−1.57244e6	+	4.40064e8i	−0.000603791	+	0.168978i
$491$	−8.93587e8	+	2.75018e9i	−0.340684	+	1.04852i	0.623170	+	0.782086i	$0.285844\pi$
$491$	−8.93587e8	+	2.75018e9i	−0.340684	+	1.04852i	−0.963854	+	0.266431i	$0.914156\pi$
$492$	−3.79670e9	−	2.75846e9i	−1.43724	−	1.04421i
$493$	−6.12215e8			−0.230112
$494$	1.76844e8	+	1.28485e8i	0.0660004	+	0.0479521i
$495$	5.29560e9	+	1.74159e9i	1.96244	+	0.645397i
$496$	2.03019e9	−	1.47502e9i	0.747053	−	0.542766i
$497$	−3.92482e8	+	2.85155e8i	−0.143408	+	0.104192i
$498$	−1.16123e8	−	3.57391e8i	−0.0421325	−	0.129670i
$499$	−4.12252e9			−1.48529			−0.742643	−	0.669687i	$-0.766428\pi$
$499$	−4.12252e9			−1.48529			−0.742643	+	0.669687i	$0.766428\pi$
$500$	2.62354e9	+	8.83643e8i	0.938628	+	0.316142i
$501$	2.37573e9			0.844044
$502$	−1.74327e7	−	5.36524e7i	−0.00615038	−	0.0189289i
$503$	2.36071e9	−	1.71515e9i	0.827093	−	0.600918i	−0.0916424	−	0.995792i	$-0.529212\pi$
$503$	2.36071e9	−	1.71515e9i	0.827093	−	0.600918i	0.918735	+	0.394874i	$0.129212\pi$
$504$	−1.43881e9	+	1.04536e9i	−0.500606	+	0.363711i
$505$	3.07478e9	+	1.01122e9i	1.06242	+	0.349402i
$506$	−8.78481e7	−	6.38254e7i	−0.0301443	−	0.0219011i
$507$	3.34750e9			1.14075
$508$	−6.27959e8	−	4.56239e8i	−0.212524	−	0.154408i
$509$	6.52407e8	−	2.00790e9i	0.219284	−	0.674886i	−0.779538	−	0.626355i	$-0.784546\pi$
$509$	6.52407e8	−	2.00790e9i	0.219284	−	0.674886i	0.998822	−	0.0485309i	$-0.0154539\pi$
$510$	−960687.	+	2.68859e8i	−0.000320691	+	0.0897490i
$511$	−1.84346e9	−	5.67359e9i	−0.611169	−	1.88098i
$512$	4.41477e8	−	1.35873e9i	0.145366	−	0.447391i
$513$	−2.16074e9	+	6.65008e9i	−0.706630	+	2.17478i
$514$	−1.39764e8	−	4.30151e8i	−0.0453968	−	0.139717i
$515$	−3.38303e9	+	1.08587e9i	−1.09139	+	0.350309i
$516$	−1.31566e9	+	4.04918e9i	−0.421569	+	1.29746i
$517$	−1.42763e9	−	1.03723e9i	−0.454358	−	0.330110i
$518$	4.44623e8			0.140552
$519$	9.29252e8	+	6.75141e8i	0.291775	+	0.211987i
$520$	−3.42885e8	+	1.10057e8i	−0.106939	+	0.0343246i
$521$	2.16687e8	−	1.57433e8i	0.0671277	−	0.0487711i	−0.553715	−	0.832706i	$-0.686790\pi$
$521$	2.16687e8	−	1.57433e8i	0.0671277	−	0.0487711i	0.620843	+	0.783935i	$0.286790\pi$
$522$	−2.12178e8	+	1.54156e8i	−0.0652909	+	0.0474366i
$523$	−1.26920e7	−	3.90620e7i	−0.00387949	−	0.0119398i	0.949098	−	0.314981i	$-0.101998\pi$
$523$	−1.26920e7	−	3.90620e7i	−0.00387949	−	0.0119398i	−0.952978	+	0.303041i	$0.901998\pi$
$524$	−1.00087e9			−0.303891
$525$	−9.36530e9	−	6.69289e7i	−2.82465	−	0.0201863i
$526$	−3.30883e8			−0.0991343
$527$	5.29689e8	+	1.63022e9i	0.157646	+	0.485186i
$528$	4.87905e9	−	3.54484e9i	1.44250	−	1.04804i
$529$	2.40736e9	−	1.74905e9i	0.707045	−	0.513698i
$530$	2.04183e6	+	2.83156e6i	0.000595737	+	0.000826153i
$531$	6.19251e9	+	4.49912e9i	1.79488	+	1.30406i
$532$	8.21397e9			2.36517
$533$	1.71160e9	+	1.24355e9i	0.489617	+	0.355728i
$534$	3.21830e8	−	9.90491e8i	0.0914602	−	0.281486i
$535$	−6.14306e9	−	2.02030e9i	−1.73439	−	0.570397i
$536$	−2.22098e7	−	6.83548e7i	−0.00622971	−	0.0191731i
$537$	−6.95164e7	+	2.13950e8i	−0.0193721	+	0.0596213i
$538$	−1.13953e8	+	3.50711e8i	−0.0315491	+	0.0970982i
$539$	2.08358e9	+	6.41260e9i	0.573125	+	1.76390i
$540$	−3.35260e9	−	4.64930e9i	−0.916227	−	1.27060i
$541$	5.71491e8	−	1.75887e9i	0.155174	−	0.477576i	−0.843005	−	0.537906i	$-0.819215\pi$
$541$	5.71491e8	−	1.75887e9i	0.155174	−	0.477576i	0.998178	+	0.0603301i	$0.0192153\pi$
$542$	−9.09083e7	−	6.60488e7i	−0.0245248	−	0.0178183i
$543$	7.27784e8			0.195076
$544$	4.72171e8	+	3.43052e8i	0.125749	+	0.0913617i
$545$	−1.24897e9	+	1.70621e9i	−0.330495	+	0.451486i
$546$	4.90441e8	−	3.56327e8i	0.128948	−	0.0936858i
$547$	−1.96797e9	+	1.42981e9i	−0.514117	+	0.373528i	−0.814383	−	0.580328i	$-0.802925\pi$
$547$	−1.96797e9	+	1.42981e9i	−0.514117	+	0.373528i	0.300266	+	0.953856i	$0.402925\pi$
$548$	−7.92861e8	−	2.44017e9i	−0.205809	−	0.633416i
$549$	−8.49716e9			−2.19165
$550$	−4.09490e8	−	2.92642e6i	−0.104948	−	0.000750009i
$551$	2.43428e9			0.619927
$552$	1.44313e8	+	4.44149e8i	0.0365189	+	0.112394i
$553$	−5.16657e9	+	3.75374e9i	−1.29917	+	0.943900i
$554$	−1.02507e8	+	7.44757e7i	−0.0256135	+	0.0186093i
$555$	−2.14173e7	+	5.99387e9i	−0.00531788	+	1.48827i
$556$	−3.39243e9	−	2.46475e9i	−0.837046	−	0.608150i
$557$	−3.96067e9			−0.971127			−0.485563	−	0.874201i	$-0.661386\pi$
$557$	−3.96067e9			−0.971127			−0.485563	+	0.874201i	$0.661386\pi$
$558$	5.94065e8	+	4.31614e8i	0.144749	+	0.105166i
$559$	5.93115e8	−	1.82542e9i	0.143614	−	0.441999i
$560$	−3.93851e9	+	5.38036e9i	−0.947706	+	1.29465i
$561$	1.27297e9	+	3.91781e9i	0.304403	+	0.936856i
$562$	−2.25903e8	+	6.95259e8i	−0.0536841	+	0.165223i
$563$	1.26506e9	−	3.89345e9i	0.298766	−	0.919507i	−0.683164	−	0.730265i	$-0.739397\pi$
$563$	1.26506e9	−	3.89345e9i	0.298766	−	0.919507i	0.981930	−	0.189243i	$-0.0606032\pi$
$564$	1.16699e9	+	3.59161e9i	0.273898	+	0.842971i
$565$	3.37734e9	−	4.61375e9i	0.787780	−	1.07618i
$566$	9.00496e7	−	2.77144e8i	0.0208749	−	0.0642463i
$567$	4.52444e9	+	3.28720e9i	1.04238	+	0.757330i
$568$	9.12288e7			0.0208888
$569$	1.83027e9	+	1.32977e9i	0.416508	+	0.302611i	0.776231	−	0.630448i	$-0.217129\pi$
$569$	1.83027e9	+	1.32977e9i	0.416508	+	0.302611i	−0.359723	+	0.933059i	$0.617129\pi$
$570$	3.81987e6	−	1.06904e9i	0.000863947	−	0.241786i
$571$	1.87873e9	−	1.36498e9i	0.422316	−	0.306831i	−0.356253	−	0.934390i	$-0.615946\pi$
$571$	1.87873e9	−	1.36498e9i	0.422316	−	0.306831i	0.778569	+	0.627559i	$0.215946\pi$
$572$	−2.22119e9	+	1.61379e9i	−0.496249	+	0.360546i
$573$	−3.89452e9	−	1.19861e10i	−0.864795	−	2.66156i
$574$	−7.67517e8			−0.169393
$575$	−5.11116e8	+	1.53563e9i	−0.112120	+	0.336859i
$576$	−8.32562e9			−1.81526
$577$	2.27168e9	+	6.99150e9i	0.492301	+	1.51515i	0.821121	+	0.570755i	$0.193349\pi$
$577$	2.27168e9	+	6.99150e9i	0.492301	+	1.51515i	−0.328819	+	0.944393i	$0.606651\pi$
$578$	2.61488e8	−	1.89982e8i	0.0563253	−	0.0409227i
$579$	−6.91273e8	+	5.02239e8i	−0.148004	+	0.107531i
$580$	−1.17870e9	+	1.61021e9i	−0.250845	+	0.342677i
$581$	5.15004e9	+	3.74173e9i	1.08942	+	0.791508i
$582$	7.33345e8			0.154198
$583$	4.32725e7	+	3.14393e7i	0.00904424	+	0.00657102i
$584$	−3.46660e8	+	1.06691e9i	−0.0720209	+	0.221658i
$585$	3.14567e9	+	4.36233e9i	0.649631	+	0.900893i
$586$	2.25047e8	+	6.92625e8i	0.0461990	+	0.142186i
$587$	2.43141e9	−	7.48310e9i	0.496163	−	1.52703i	−0.318974	−	0.947763i	$-0.603338\pi$
$587$	2.43141e9	−	7.48310e9i	0.496163	−	1.52703i	0.815137	−	0.579268i	$-0.196662\pi$
$588$	4.45899e9	−	1.37234e10i	0.904515	−	2.78381i
$589$	−2.10615e9	−	6.48205e9i	−0.424702	−	1.30710i
$590$	−5.34130e8	−	1.75662e8i	−0.107069	−	0.0352124i
$591$	−1.17649e9	+	3.62087e9i	−0.234440	+	0.721533i
$592$	3.45239e9	+	2.50831e9i	0.683902	+	0.496884i
$593$	4.87014e9			0.959069			0.479534	−	0.877523i	$-0.340806\pi$
$593$	4.87014e9			0.959069			0.479534	+	0.877523i	$0.340806\pi$
$594$	6.85957e8	+	4.98377e8i	0.134290	+	0.0975675i
$595$	−2.66390e9	−	3.69424e9i	−0.518453	−	0.718978i
$596$	−1.25871e9	+	9.14506e8i	−0.243536	+	0.176940i
$597$	−1.50542e9	+	1.09375e9i	−0.289566	+	0.210382i
$598$	−3.23727e7	−	9.96330e7i	−0.00619049	−	0.0190524i
$599$	6.77105e8			0.128725			0.0643624	−	0.997927i	$-0.479499\pi$
$599$	6.77105e8			0.128725			0.0643624	+	0.997927i	$0.479499\pi$
$600$	1.41739e9	+	1.04535e9i	0.267891	+	0.197575i
$601$	6.69738e9			1.25847			0.629237	−	0.777213i	$-0.283367\pi$
$601$	6.69738e9			1.25847			0.629237	+	0.777213i	$0.283367\pi$
$602$	2.15170e8	+	6.62226e8i	0.0401971	+	0.123714i
$603$	−8.68396e8	+	6.30926e8i	−0.161290	+	0.117184i
$604$	1.97586e9	−	1.43555e9i	0.364860	−	0.265087i
$605$	−7.87856e8	+	2.52881e8i	−0.144645	+	0.0464272i
$606$	8.28956e8	+	6.02272e8i	0.151313	+	0.109936i
$607$	6.30172e7			0.0114366			0.00571832	−	0.999984i	$-0.498180\pi$
$607$	6.30172e7			0.0114366			0.00571832	+	0.999984i	$0.498180\pi$
$608$	−1.87744e9	−	1.36404e9i	−0.338769	−	0.246130i
$609$	2.08617e9	−	6.42058e9i	0.374274	−	1.15190i
$610$	5.94320e8	−	1.90761e8i	0.106015	−	0.0340279i
$611$	−5.26092e8	−	1.61914e9i	−0.0933076	−	0.287171i
$612$	1.79281e9	−	5.51772e9i	0.316159	−	0.973037i
$613$	−1.59149e9	+	4.89809e9i	−0.279056	+	0.858846i	0.709061	+	0.705147i	$0.249119\pi$
$613$	−1.59149e9	+	4.89809e9i	−0.279056	+	0.858846i	−0.988118	+	0.153700i	$0.950881\pi$
$614$	2.62253e8	+	8.07133e8i	0.0457227	+	0.140720i
$615$	3.69709e7	−	1.03467e10i	0.00640910	−	1.79366i
$616$	6.18551e8	−	1.90370e9i	0.106621	−	0.328146i
$617$	3.03979e9	+	2.20854e9i	0.521010	+	0.378536i	0.816984	−	0.576660i	$-0.195644\pi$
$617$	3.03979e9	+	2.20854e9i	0.521010	+	0.378536i	−0.295974	+	0.955196i	$0.595644\pi$
$618$	−1.12475e9			−0.191689
$619$	−9.16549e9	−	6.65912e9i	−1.55324	−	1.12849i	−0.941290	−	0.337598i	$-0.890386\pi$
$619$	−9.16549e9	−	6.65912e9i	−1.55324	−	1.12849i	−0.611950	−	0.790897i	$-0.709614\pi$
$620$	5.30751e9	+	1.74551e9i	0.894375	+	0.294137i
$621$	2.71108e9	−	1.96971e9i	0.454277	−	0.330052i
$622$	6.70237e8	−	4.86956e8i	0.111677	−	0.0811378i
$623$	5.45183e9	+	1.67790e10i	0.903305	+	2.78009i
$624$	5.81835e9			0.958636
$625$	1.80293e9	+	5.83115e9i	0.295393	+	0.955376i
$626$	−3.88476e8			−0.0632928
$627$	−5.06158e9	−	1.55779e10i	−0.820068	−	2.52391i
$628$	−8.13942e9	+	5.91363e9i	−1.31140	+	0.952787i
$629$	−2.35819e9	+	1.71332e9i	−0.377834	+	0.274513i
$630$	−1.85345e9	−	6.09553e8i	−0.295317	−	0.0971224i
$631$	3.73588e9	+	2.71428e9i	0.591958	+	0.430082i	0.843015	−	0.537890i	$-0.180778\pi$
$631$	3.73588e9	+	2.71428e9i	0.591958	+	0.430082i	−0.251058	+	0.967972i	$0.580778\pi$
$632$	1.20092e9			0.189236
$633$	−1.62766e9	−	1.18257e9i	−0.255065	−	0.185316i
$634$	1.85506e6	−	5.70930e6i	0.000289099	−	0.000889755i
$635$	6.11485e6	−	1.71131e9i	0.000947715	−	0.265229i
$636$	−3.53723e7	−	1.08865e8i	−0.00545209	−	0.0167798i
$637$	−2.01017e9	+	6.18666e9i	−0.308137	+	0.948349i
$638$	9.12162e7	−	2.80735e8i	0.0139059	−	0.0427980i
$639$	−4.21029e8	−	1.29579e9i	−0.0638350	−	0.196464i
$640$	2.41116e9	−	7.73919e8i	0.363577	−	0.116699i
$641$	−3.43300e9	+	1.05657e10i	−0.514838	+	1.58451i	0.268737	+	0.963213i	$0.413394\pi$
$641$	−3.43300e9	+	1.05657e10i	−0.514838	+	1.58451i	−0.783576	+	0.621296i	$0.786606\pi$
$642$	−1.65616e9	−	1.20327e9i	−0.247019	−	0.179469i
$643$	9.32929e9			1.38392			0.691958	−	0.721937i	$-0.256748\pi$
$643$	9.32929e9			1.38392			0.691958	+	0.721937i	$0.256748\pi$
$644$	−3.18474e9	−	2.31385e9i	−0.469866	−	0.341378i
$645$	−8.93770e9	+	2.86877e9i	−1.31150	+	0.420956i
$646$	4.20595e8	−	3.05580e8i	0.0613833	−	0.0445976i
$647$	−8.49682e9	+	6.17330e9i	−1.23337	+	0.896092i	−0.997138	−	0.0756055i	$-0.975911\pi$
$647$	−8.49682e9	+	6.17330e9i	−1.23337	+	0.896092i	−0.236227	+	0.971698i	$0.575911\pi$
$648$	−3.24982e8	−	1.00019e9i	−0.0469188	−	0.144401i
$649$	−8.61504e9			−1.23709
$650$	−3.17953e8	−	2.34496e8i	−0.0454115	−	0.0334918i
$651$	−1.89018e10			−2.68515
$652$	−1.79603e9	−	5.52761e9i	−0.253774	−	0.781036i
$653$	3.85977e9	−	2.80429e9i	0.542457	−	0.394118i	−0.282540	−	0.959256i	$-0.591177\pi$
$653$	3.85977e9	−	2.80429e9i	0.542457	−	0.394118i	0.824997	+	0.565138i	$0.191177\pi$
$654$	−5.41529e8	+	3.93444e8i	−0.0757007	+	0.0549998i
$655$	−1.29066e9	−	1.78985e9i	−0.179459	−	0.248870i
$656$	−5.95959e9	−	4.32989e9i	−0.824238	−	0.598844i
$657$	1.67540e10			2.30484
$658$	4.99667e8	+	3.63029e8i	0.0683738	+	0.0496765i
$659$	3.08991e9	−	9.50976e9i	0.420578	−	1.29441i	−0.486587	−	0.873632i	$-0.661758\pi$
$659$	3.08991e9	−	9.50976e9i	0.420578	−	1.29441i	0.907165	−	0.420774i	$-0.138242\pi$
$660$	1.27552e10	+	4.19488e9i	1.72697	+	0.567957i
$661$	3.21280e8	+	9.88798e8i	0.0432692	+	0.133169i	0.970357	−	0.241674i	$-0.0776966\pi$
$661$	3.21280e8	+	9.88798e8i	0.0432692	+	0.133169i	−0.927088	+	0.374843i	$0.877697\pi$
$662$	−5.07728e7	+	1.56262e8i	−0.00680186	+	0.0209340i
$663$	−1.22812e9	+	3.77977e9i	−0.163660	+	0.503695i
$664$	−3.69918e8	−	1.13849e9i	−0.0490362	−	0.150918i
$665$	1.05922e10	+	1.46890e10i	1.39672	+	1.93694i
$666$	−3.85870e8	+	1.18759e9i	−0.0506152	+	0.155778i
$667$	−9.43827e8	−	6.85731e8i	−0.123155	−	0.0894774i
$668$	3.76584e9			0.488814
$669$	1.15061e10	+	8.35970e9i	1.48572	+	1.07944i
$670$	4.65742e7	−	6.36246e7i	0.00598251	−	0.00817265i
$671$	7.73712e9	−	5.62134e9i	0.988668	−	0.718309i
$672$	−5.20670e9	+	3.78289e9i	−0.661867	+	0.480874i
$673$	1.05879e9	+	3.25861e9i	0.133892	+	0.412079i	0.995416	−	0.0956389i	$-0.0304894\pi$
$673$	1.05879e9	+	3.25861e9i	0.133892	+	0.412079i	−0.861524	+	0.507717i	$0.830489\pi$
$674$	7.00474e8			0.0881216
$675$	3.99102e9	−	1.19908e10i	0.499483	−	1.50068i
$676$	5.30621e9			0.660649
$677$	−3.69884e9	−	1.13839e10i	−0.458148	−	1.41003i	−0.867400	−	0.497612i	$-0.834210\pi$
$677$	−3.69884e9	−	1.13839e10i	−0.458148	−	1.41003i	0.409252	−	0.912421i	$-0.365790\pi$
$678$	1.46435e9	−	1.06391e9i	0.180443	−	0.131100i
$679$	−1.00504e10	+	7.30202e9i	−1.23208	+	0.895157i
$680$	−3.06032e6	+	8.56467e8i	−0.000373238	+	0.104455i
$681$	−3.27965e9	−	2.38280e9i	−0.397935	−	0.289117i
$682$	−8.26465e8			−0.0997652
$683$	−7.05134e9	−	5.12310e9i	−0.846835	−	0.615262i	0.0774364	−	0.996997i	$-0.475327\pi$
$683$	−7.05134e9	−	5.12310e9i	−0.846835	−	0.615262i	−0.924272	+	0.381735i	$0.875327\pi$
$684$	−7.12857e9	+	2.19395e10i	−0.851738	+	2.62138i
$685$	3.34133e9	−	4.56455e9i	0.397193	−	0.542602i
$686$	−3.07243e8	−	9.45597e8i	−0.0363369	−	0.111833i
$687$	−3.77913e9	+	1.16310e10i	−0.444675	+	1.36857i
$688$	−2.06516e9	+	6.35590e9i	−0.241765	+	0.744076i
$689$	1.59463e7	+	4.90775e7i	0.00185734	+	0.00571630i
$690$	−3.02625e8	+	4.13413e8i	−0.0350698	+	0.0479085i
$691$	5.45994e8	−	1.68040e9i	0.0629528	−	0.193749i	−0.914633	−	0.404284i	$-0.867521\pi$
$691$	5.45994e8	−	1.68040e9i	0.0629528	−	0.193749i	0.977586	+	0.210535i	$0.0675207\pi$
$692$	1.47298e9	+	1.07018e9i	0.168977	+	0.122769i
$693$	−2.98944e10			−3.41212
$694$	1.32031e9	+	9.59261e8i	0.149940	+	0.108938i
$695$	3.30343e7	−	9.24504e9i	0.00373266	−	1.04463i
$696$	−1.02706e9	+	7.46201e8i	−0.115468	+	0.0838926i
$697$	4.07076e9	−	2.95758e9i	0.455366	−	0.330843i
$698$	2.80190e8	+	8.62338e8i	0.0311860	+	0.0959806i
$699$	2.08054e10			2.30412
$700$	−1.48452e10	−	1.06091e8i	−1.63585	−	0.0116905i
$701$	−5.42431e9			−0.594746			−0.297373	−	0.954761i	$-0.596110\pi$
$701$	−5.42431e9			−0.594746			−0.297373	+	0.954761i	$0.596110\pi$
$702$	2.52780e8	+	7.77978e8i	0.0275780	+	0.0848765i
$703$	9.37661e9	−	6.81251e9i	1.01789	−	0.739543i
$704$	7.58093e9	−	5.50786e9i	0.818876	−	0.594948i
$705$	−4.91799e9	+	6.71841e9i	−0.528598	+	0.722113i
$706$	2.03594e8	+	1.47920e8i	0.0217745	+	0.0158201i
$707$	−1.73576e10			−1.84723
$708$	1.49156e10	+	1.08368e10i	1.57952	+	1.14759i
$709$	−4.88086e9	+	1.50217e10i	−0.514321	+	1.58292i	0.270193	+	0.962806i	$0.412913\pi$
$709$	−4.88086e9	+	1.50217e10i	−0.514321	+	1.58292i	−0.784514	+	0.620111i	$0.787087\pi$
$710$	5.85387e7	+	8.11800e7i	0.00613817	+	0.00851226i
$711$	−5.54236e9	−	1.70576e10i	−0.578297	−	1.77981i
$712$	1.02521e9	−	3.15527e9i	0.106447	−	0.327609i
$713$	−1.00937e9	+	3.10653e9i	−0.104289	+	0.320968i
$714$	−4.45538e8	−	1.37123e9i	−0.0458080	−	0.140982i
$715$	−5.75022e9	−	1.89110e9i	−0.588320	−	0.193484i
$716$	−1.10192e8	+	3.39137e8i	−0.0112190	+	0.0345287i
$717$	2.06256e10	+	1.49854e10i	2.08973	+	1.51828i
$718$	−2.93712e8			−0.0296133
$719$	−3.78712e9	−	2.75151e9i	−0.379978	−	0.276070i	0.381358	−	0.924427i	$-0.375456\pi$
$719$	−3.78712e9	−	2.75151e9i	−0.379978	−	0.276070i	−0.761336	+	0.648357i	$0.775456\pi$
$720$	−1.09528e10	−	1.51891e10i	−1.09361	−	1.51659i
$721$	1.54146e10	−	1.11993e10i	1.53164	−	1.11280i
$722$	−8.72322e8	+	6.33779e8i	−0.0862575	+	0.0626697i
$723$	5.57559e8	+	1.71599e9i	0.0548665	+	0.168862i
$724$	1.15363e9			0.112975
$725$	−4.39951e9	−	3.14410e7i	−0.428767	−	0.00306417i
$726$	−2.61938e8			−0.0254050
$727$	−2.35343e9	−	7.24312e9i	−0.227160	−	0.699126i	−0.998065	−	0.0621761i	$-0.980196\pi$
$727$	−2.35343e9	−	7.24312e9i	−0.227160	−	0.699126i	0.770906	−	0.636950i	$-0.219804\pi$
$728$	1.56233e9	−	1.13510e9i	0.150077	−	0.109037i
$729$	1.01837e10	−	7.39893e9i	0.973557	−	0.707330i
$730$	−1.17183e9	+	3.76127e8i	−0.111490	+	0.0357853i
$731$	−3.69307e9	−	2.68317e9i	−0.349684	−	0.254061i
$732$	−2.04667e10			−1.92867
$733$	−4.63202e9	−	3.36536e9i	−0.434417	−	0.315622i	0.348996	−	0.937124i	$-0.386523\pi$
$733$	−4.63202e9	−	3.36536e9i	−0.434417	−	0.315622i	−0.783412	+	0.621502i	$0.786523\pi$
$734$	−2.43565e7	+	7.49615e7i	−0.00227341	+	0.00699684i
$735$	3.02914e10	−	9.72275e9i	2.81393	−	0.903199i
$736$	3.43680e8	+	1.05774e9i	0.0317748	+	0.0977927i
$737$	3.73328e8	−	1.14898e9i	0.0343521	−	0.105725i
$738$	6.66097e8	−	2.05004e9i	0.0610015	−	0.187743i
$739$	1.11259e9	+	3.42419e9i	0.101410	+	0.312106i	0.988871	−	0.148775i	$-0.0475332\pi$
$739$	1.11259e9	+	3.42419e9i	0.101410	+	0.312106i	−0.887461	+	0.460882i	$0.847533\pi$
$740$	−3.39491e7	+	9.50104e9i	−0.00307976	+	0.861907i
$741$	4.88324e9	−	1.50291e10i	0.440905	−	1.35696i
$742$	−1.51453e7	−	1.10037e7i	−0.00136102	−	0.000988838i
$743$	3.37757e9			0.302095			0.151047	−	0.988527i	$-0.451735\pi$
$743$	3.37757e9			0.302095			0.151047	+	0.988527i	$0.451735\pi$
$744$	2.87561e9	+	2.08925e9i	0.255991	+	0.185988i
$745$	−3.25855e9	−	1.07166e9i	−0.288721	−	0.0949529i
$746$	3.00458e8	−	2.18296e8i	0.0264971	−	0.0192513i
$747$	−1.44637e10	+	1.05085e10i	−1.26957	+	0.922395i
$748$	2.01782e9	+	6.21022e9i	0.176290	+	0.542565i
$749$	3.46785e10			3.01560
$750$	−2.07113e7	+	1.93203e9i	−0.00179264	+	0.167224i
$751$	2.03411e10			1.75240			0.876201	−	0.481945i	$-0.160070\pi$
$751$	2.03411e10			1.75240			0.876201	+	0.481945i	$0.160070\pi$
$752$	1.83179e9	+	5.63767e9i	0.157077	+	0.483434i
$753$	−3.29939e9	+	2.39714e9i	−0.281612	+	0.204603i
$754$	2.30393e8	−	1.67390e8i	0.0195736	−	0.0142210i
$755$	5.11511e9	+	1.68223e9i	0.432554	+	0.142256i
$756$	2.48679e10	+	1.80676e10i	2.09321	+	1.52080i
$757$	1.84468e9			0.154556			0.0772780	−	0.997010i	$-0.475377\pi$
$757$	1.84468e9			0.154556			0.0772780	+	0.997010i	$0.475377\pi$
$758$	−1.71403e9	−	1.24532e9i	−0.142948	−	0.103858i
$759$	−2.42577e9	+	7.46576e9i	−0.201374	+	0.619766i
$760$	1.21684e7	−	3.40548e9i	0.00100551	−	0.281404i
$761$	−6.37404e9	−	1.96173e10i	−0.524287	−	1.61359i	−0.765722	−	0.643171i	$-0.777618\pi$
$761$	−6.37404e9	−	1.96173e10i	−0.524287	−	1.61359i	0.241436	−	0.970417i	$-0.422382\pi$
$762$	1.67407e8	−	5.15225e8i	0.0137066	−	0.0421846i
$763$	3.50399e9	−	1.07842e10i	0.285579	−	0.878923i
$764$	−6.17331e9	−	1.89995e10i	−0.500831	−	1.54140i
$765$	1.21792e10	−	3.90920e9i	0.983565	−	0.315699i
$766$	−3.06683e7	+	9.43874e7i	−0.00246541	+	0.00758776i
$767$	−6.72414e9	−	4.88537e9i	−0.538088	−	0.390944i
$768$	−1.94455e10			−1.54901
$769$	−8.26027e9	−	6.00144e9i	−0.655016	−	0.475897i	0.209960	−	0.977710i	$-0.432667\pi$
$769$	−8.26027e9	−	6.00144e9i	−0.655016	−	0.475897i	−0.864976	+	0.501813i	$0.832667\pi$
$770$	2.09092e9	−	6.71130e8i	0.165051	−	0.0529772i
$771$	−2.64524e10	+	1.92188e10i	−2.07862	+	1.51020i
$772$	−1.09576e9	+	7.96113e8i	−0.0857143	+	0.0622751i
$773$	−6.86161e9	−	2.11179e10i	−0.534315	−	1.64445i	−0.745124	−	0.666926i	$-0.767610\pi$
$773$	−6.86161e9	−	2.11179e10i	−0.534315	−	1.64445i	0.210808	−	0.977527i	$-0.432390\pi$
$774$	−1.95554e9			−0.151591
$775$	3.72273e9	+	1.17423e10i	0.287280	+	0.906142i
$776$	2.33611e9			0.179464
$777$	−9.93269e9	−	3.05697e10i	−0.759615	−	2.33785i
$778$	−1.68539e9	+	1.22451e9i	−0.128313	+	0.0932252i
$779$	−1.61861e10	+	1.17599e10i	−1.22676	+	0.891296i
$780$	7.57681e9	+	1.05073e10i	0.571683	+	0.792796i
$781$	1.24061e9	+	9.01355e8i	0.0931872	+	0.0677044i
$782$	−2.49155e8			−0.0186314
$783$	7.36982e9	+	5.35449e9i	0.548644	+	0.398613i
$784$	6.99917e9	−	2.15412e10i	0.518729	−	1.59648i
$785$	−2.10714e10	−	6.92984e9i	−1.55471	−	0.511304i
$786$	−2.15862e8	−	6.64356e8i	−0.0158562	−	0.0488002i
$787$	−7.45903e9	+	2.29565e10i	−0.545470	+	1.67878i	0.174401	+	0.984675i	$0.444201\pi$
$787$	−7.45903e9	+	2.29565e10i	−0.545470	+	1.67878i	−0.719871	+	0.694108i	$0.755799\pi$
$788$	−1.86489e9	+	5.73953e9i	−0.135772	+	0.417864i
$789$	7.39178e9	+	2.27496e10i	0.535771	+	1.64893i
$790$	7.70594e8	+	1.06864e9i	0.0556072	+	0.0771147i
$791$	−9.47513e9	+	2.91614e10i	−0.680718	+	2.09503i
$792$	4.54797e9	+	3.30429e9i	0.325296	+	0.236342i
$793$	9.22664e9			0.657033
$794$	8.27346e8	+	6.01102e8i	0.0586564	+	0.0426164i
$795$	1.49068e8	−	2.03640e8i	0.0105220	−	0.0143740i
$796$	−2.38629e9	+	1.73374e9i	−0.167698	+	0.121839i
$797$	5.21169e9	−	3.78651e9i	0.364648	−	0.264933i	−0.390340	−	0.920671i	$-0.627643\pi$
$797$	5.21169e9	−	3.78651e9i	0.364648	−	0.264933i	0.754988	+	0.655738i	$0.227643\pi$
$798$	1.77154e9	+	5.45225e9i	0.123408	+	0.379810i
$799$	−4.04904e9			−0.280827
$800$	3.37550e9	+	2.48949e9i	0.233090	+	0.171908i
$801$	−4.95481e10			−3.40654
$802$	−3.20107e8	−	9.85187e8i	−0.0219121	−	0.0674385i
$803$	−1.52554e10	+	1.10837e10i	−1.03973	+	0.755407i
$804$	−2.09166e9	+	1.51968e9i	−0.141937	+	0.103123i
$805$	3.10119e7	−	8.67904e9i	0.00209528	−	0.586390i
$806$	−6.45066e8	−	4.68668e8i	−0.0433942	−	0.0315277i
$807$	2.66585e10			1.78558
$808$	2.64069e9	+	1.91857e9i	0.176107	+	0.127949i
$809$	−3.90190e9	+	1.20088e10i	−0.259093	+	0.797407i	0.733902	+	0.679255i	$0.237697\pi$
$809$	−3.90190e9	+	1.20088e10i	−0.259093	+	0.797407i	−0.992996	+	0.118152i	$0.962303\pi$
$810$	6.81491e8	−	9.30978e8i	0.0450570	−	0.0615519i
$811$	2.32423e9	+	7.15324e9i	0.153005	+	0.470901i	0.997953	−	0.0639469i	$-0.0203688\pi$
$811$	2.32423e9	+	7.15324e9i	0.153005	+	0.470901i	−0.844948	+	0.534848i	$0.820369\pi$
$812$	3.30685e9	−	1.01774e10i	0.216754	−	0.667102i
$813$	−2.51027e9	+	7.72583e9i	−0.163834	+	0.504229i
$814$	−4.34299e8	−	1.33664e9i	−0.0282230	−	0.0868615i
$815$	7.56895e9	−	1.03399e10i	0.489761	−	0.669057i
$816$	4.27617e9	−	1.31607e10i	0.275511	−	0.847937i
$817$	1.46843e10	+	1.06688e10i	0.942057	+	0.684444i
$818$	−2.83581e9			−0.181151
$819$	−2.33330e10	−	1.69524e10i	−1.48415	−	1.07829i
$820$	5.86036e7	−	1.64009e10i	0.00371173	−	1.03877i
$821$	1.99093e10	−	1.44650e10i	1.25561	−	0.912255i	0.257078	−	0.966391i	$-0.417240\pi$
$821$	1.99093e10	−	1.44650e10i	1.25561	−	0.912255i	0.998534	+	0.0541359i	$0.0172404\pi$
$822$	1.44873e9	−	1.05257e9i	0.0909782	−	0.0660995i
$823$	5.19380e9	+	1.59849e10i	0.324777	+	0.999561i	0.971541	+	0.236871i	$0.0761219\pi$
$823$	5.19380e9	+	1.59849e10i	0.324777	+	0.999561i	−0.646764	+	0.762690i	$0.723878\pi$
$824$	−3.58297e9			−0.223099
$825$	8.94664e9	+	2.82195e10i	0.554717	+	1.74969i
$826$	3.01525e9			0.186163
$827$	2.57111e9	+	7.91305e9i	0.158071	+	0.486491i	0.998459	−	0.0554934i	$-0.0176732\pi$
$827$	2.57111e9	+	7.91305e9i	0.158071	+	0.486491i	−0.840389	+	0.541984i	$0.817673\pi$
$828$	8.94420e9	−	6.49834e9i	0.547564	−	0.397829i
$829$	−1.51591e10	+	1.10137e10i	−0.924130	+	0.671420i	−0.944549	−	0.328372i	$-0.893500\pi$
$829$	−1.51591e10	+	1.10137e10i	−0.924130	+	0.671420i	0.0204186	+	0.999792i	$0.493500\pi$
$830$	7.75721e8	−	1.05971e9i	0.0470904	−	0.0643297i
$831$	7.41048e9	+	5.38403e9i	0.447964	+	0.325465i
$832$	9.04038e9			0.544196
$833$	1.25164e10	+	9.09372e9i	0.750279	+	0.545110i
$834$	9.04383e8	−	2.78340e9i	0.0539848	−	0.166148i
$835$	4.85617e9	+	6.73442e9i	0.288663	+	0.400311i
$836$	−8.02325e9	−	2.46930e10i	−0.474929	−	1.46168i
$837$	7.88163e9	−	2.42572e10i	0.464598	−	1.42988i
$838$	1.35765e8	−	4.17841e8i	0.00796953	−	0.0245277i
$839$	−7.73188e9	−	2.37963e10i	−0.451979	−	1.39105i	−0.874646	−	0.484763i	$-0.838906\pi$
$839$	−7.73188e9	−	2.37963e10i	−0.451979	−	1.39105i	0.422667	−	0.906285i	$-0.361094\pi$
$840$	−8.97172e9	−	2.95057e9i	−0.522274	−	0.171763i
$841$	−4.35049e9	+	1.33894e10i	−0.252204	+	0.776205i
$842$	1.28609e8	+	9.34400e7i	0.00742471	+	0.00539437i
$843$	5.28486e10			3.03834
$844$	−2.58005e9	−	1.87452e9i	−0.147717	−	0.107322i
$845$	6.84253e9	+	9.48905e9i	0.390138	+	0.541034i
$846$	−1.40329e9	+	1.01955e9i	−0.0796803	+	0.0578911i
$847$	3.58981e9	−	2.60815e9i	0.202992	−	0.147483i
$848$	−5.55230e7	−	1.70882e8i	−0.00312671	−	0.00962302i
$849$	−2.10665e10			−1.18145
$850$	−7.64092e8	+	5.46845e8i	−0.0426756	+	0.0305420i
$851$	−5.55459e9			−0.308957
$852$	−1.01411e9	−	3.12111e9i	−0.0561755	−	0.172890i
$853$	−1.36724e10	+	9.93357e9i	−0.754263	+	0.548004i	−0.897145	−	0.441735i	$-0.854363\pi$
$853$	−1.36724e10	+	9.93357e9i	−0.754263	+	0.548004i	0.142882	+	0.989740i	$0.454363\pi$
$854$	−2.70798e9	+	1.96746e9i	−0.148779	+	0.108094i
$855$	−4.84268e10	+	1.55437e10i	−2.64975	+	0.850499i
$856$	−5.27579e9	−	3.83309e9i	−0.287494	−	0.208877i
$857$	−7.05846e9			−0.383069			−0.191534	−	0.981486i	$-0.561346\pi$
$857$	−7.05846e9			−0.383069			−0.191534	+	0.981486i	$0.561346\pi$
$858$	−1.55025e9	−	1.12632e9i	−0.0837908	−	0.0608776i
$859$	1.81620e7	−	5.58970e7i	0.000977661	−	0.00300893i	−0.950566	−	0.310521i	$-0.899496\pi$
$859$	1.81620e7	−	5.58970e7i	0.000977661	−	0.00300893i	0.951544	+	0.307512i	$0.0994965\pi$
$860$	−1.41674e10	+	4.54736e9i	−0.759531	+	0.243789i
$861$	1.71460e10	+	5.27700e10i	0.915487	+	2.81758i
$862$	2.46918e8	−	7.59935e8i	0.0131304	−	0.0404111i
$863$	8.06411e9	−	2.48188e10i	0.427089	−	1.31445i	−0.473890	−	0.880584i	$-0.657151\pi$
$863$	8.06411e9	−	2.48188e10i	0.427089	−	1.31445i	0.900980	−	0.433862i	$-0.142849\pi$
$864$	−2.68361e9	−	8.25930e9i	−0.141554	−	0.435657i
$865$	−1.43434e7	+	4.01416e9i	−0.000753521	+	0.210882i
$866$	−3.31561e8	+	1.02044e9i	−0.0173480	+	0.0533918i
$867$	−1.89036e10	−	1.37342e10i	−0.985092	−	0.715711i
$868$	−2.99617e10			−1.55506
$869$	1.63312e10	+	1.18653e10i	0.844206	+	0.613351i
$870$	−1.32304e9	−	4.35114e8i	−0.0681170	−	0.0224019i
$871$	9.42947e8	−	6.85091e8i	0.0483530	−	0.0351305i
$872$	−1.72507e9	+	1.25334e9i	−0.0881048	+	0.0640119i
$873$	−1.07814e10	−	3.31816e10i	−0.548433	−	1.68790i
$874$	9.90688e8			0.0501934
$875$	−1.89536e10	−	2.66844e10i	−0.956455	−	1.34657i
$876$	4.03546e10			2.02828
$877$	1.47345e9	+	4.53482e9i	0.0737629	+	0.227019i	0.981140	−	0.193299i	$-0.0619187\pi$
$877$	1.47345e9	+	4.53482e9i	0.0737629	+	0.227019i	−0.907377	+	0.420318i	$0.861919\pi$
$878$	−1.07081e9	+	7.77992e8i	−0.0533929	+	0.0387922i
$879$	4.25934e10	−	3.09459e10i	2.11534	−	1.53689i
$880$	2.00216e10	+	6.58460e9i	0.990397	+	0.325717i
$881$	−5.65364e9	−	4.10761e9i	−0.278556	−	0.202383i	0.439731	−	0.898129i	$-0.355074\pi$
$881$	−5.65364e9	−	4.10761e9i	−0.278556	−	0.202383i	−0.718287	+	0.695746i	$0.755074\pi$
$882$	6.62766e9			0.325252
$883$	−1.64806e10	−	1.19738e10i	−0.805583	−	0.585290i	0.106964	−	0.994263i	$-0.465887\pi$
$883$	−1.64806e10	−	1.19738e10i	−0.805583	−	0.585290i	−0.912547	+	0.408973i	$0.865887\pi$
$884$	−1.94673e9	+	5.99141e9i	−0.0947812	+	0.291707i
$885$	−1.45243e8	+	4.06479e10i	−0.00704358	+	1.97123i
$886$	−7.94639e8	−	2.44565e9i	−0.0383842	−	0.118134i
$887$	7.60522e9	−	2.34065e10i	0.365914	−	1.12617i	−0.583492	−	0.812119i	$-0.698314\pi$
$887$	7.60522e9	−	2.34065e10i	0.365914	−	1.12617i	0.949407	−	0.314050i	$-0.101686\pi$
$888$	−1.86783e9	+	5.74858e9i	−0.0895140	+	0.275496i
$889$	2.83589e9	+	8.72796e9i	0.135373	+	0.416636i
$890$	3.46556e9	−	1.11235e9i	0.164781	−	0.0528906i
$891$	5.46266e9	−	1.68124e10i	0.258721	−	0.796263i
$892$	1.82387e10	+	1.32512e10i	0.860432	+	0.625140i
$893$	1.60998e10			0.756552
$894$	−8.78501e8	−	6.38268e8i	−0.0411207	−	0.0298760i
$895$	−7.48573e8	+	2.40272e8i	−0.0349023	+	0.0112027i
$896$	−1.09863e10	+	7.98200e9i	−0.510238	+	0.370709i
$897$	−6.12699e9	+	4.45152e9i	−0.283448	+	0.205937i
$898$	−8.20725e8	−	2.52593e9i	−0.0378208	−	0.116400i
$899$	−8.87942e9			−0.407592
$900$	1.31669e10	−	3.95594e10i	0.602053	−	1.80884i
$901$	1.22730e8			0.00559001
$902$	7.49696e8	+	2.30733e9i	0.0340144	+	0.104685i
$903$	4.07240e10	−	2.95877e10i	1.84053	−	1.33723i
$904$	4.66476e9	−	3.38915e9i	0.210010	−	0.152581i
$905$	1.48764e9	+	2.06303e9i	0.0667158	+	0.0925199i
$906$	1.37903e9	+	1.00192e9i	0.0616061	+	0.0447594i
$907$	6.68356e9			0.297428			0.148714	−	0.988880i	$-0.452487\pi$
$907$	6.68356e9			0.297428			0.148714	+	0.988880i	$0.452487\pi$
$908$	−5.19866e9	−	3.77705e9i	−0.230458	−	0.167437i
$909$	1.50640e10	−	4.63621e10i	0.665220	−	2.04734i
$910$	2.01257e9	+	6.61883e8i	0.0885331	+	0.0291163i
$911$	1.12979e10	+	3.47712e10i	0.495087	+	1.52372i	0.816821	+	0.576891i	$0.195734\pi$
$911$	1.12979e10	+	3.47712e10i	0.495087	+	1.52372i	−0.321734	+	0.946830i	$0.604266\pi$
$912$	−1.70029e10	+	5.23295e10i	−0.742233	+	2.28436i
$913$	6.21800e9	−	1.91370e10i	0.270397	−	0.832198i
$914$	1.37167e8	+	4.22157e8i	0.00594208	+	0.0182878i
$915$	−2.63925e10	−	3.66004e10i	−1.13895	−	1.57947i
$916$	−5.99040e9	+	1.84365e10i	−0.257526	+	0.792584i
$917$	9.57344e9	+	6.95551e9i	0.409992	+	0.297877i
$918$	1.94551e9			0.0830012
$919$	3.45882e10	+	2.51298e10i	1.47002	+	1.06803i	0.980607	+	0.195985i	$0.0627902\pi$
$919$	3.45882e10	+	2.51298e10i	1.47002	+	1.06803i	0.489417	+	0.872050i	$0.337210\pi$
$920$	−9.64030e8	+	1.31695e9i	−0.0408163	+	0.0557587i
$921$	4.96351e10	−	3.60620e10i	2.09354	−	1.52104i
$922$	−1.23675e9	+	8.98551e8i	−0.0519665	+	0.0377559i
$923$	4.57174e8	+	1.40704e9i	0.0191371	+	0.0588978i
$924$	−7.20053e10			−3.00270
$925$	−1.70344e10	+	1.21912e10i	−0.707671	+	0.506466i
$926$	−3.75804e9			−0.155533
$927$	1.65357e10	+	5.08917e10i	0.681779	+	2.09830i
$928$	−2.44594e9	+	1.77708e9i	−0.100468	+	0.0729942i
$929$	−1.55290e10	+	1.12825e10i	−0.635462	+	0.461690i	−0.858288	−	0.513168i	$-0.828472\pi$
$929$	−1.55290e10	+	1.12825e10i	−0.635462	+	0.461690i	0.222826	+	0.974858i	$0.428472\pi$
$930$	−1.39336e7	+	3.89947e9i	−0.000568031	+	0.158970i
$931$	−4.97677e10	−	3.61584e10i	−2.02127	−	1.46854i
$932$	3.29792e10			1.33439
$933$	−4.84531e10	−	3.52032e10i	−1.95315	−	1.41905i
$934$	−8.64188e8	+	2.65970e9i	−0.0347052	+	0.106812i
$935$	−8.50365e9	+	1.16167e10i	−0.340224	+	0.464776i
$936$	1.67596e9	+	5.15808e9i	0.0668034	+	0.205600i
$937$	7.03441e9	−	2.16497e10i	0.279344	−	0.859732i	−0.708693	−	0.705517i	$-0.750715\pi$
$937$	7.03441e9	−	2.16497e10i	0.279344	−	0.859732i	0.988037	−	0.154216i	$-0.0492850\pi$
$938$	−1.30664e8	+	4.02142e8i	−0.00516947	+	0.0159100i
$939$	8.67840e9	+	2.67094e10i	0.342066	+	1.05277i
$940$	−7.79564e9	+	1.06495e10i	−0.306129	+	0.418199i
$941$	−3.55264e9	+	1.09339e10i	−0.138991	+	0.427772i	−0.996189	−	0.0872153i	$-0.972203\pi$
$941$	−3.55264e9	+	1.09339e10i	−0.138991	+	0.427772i	0.857198	+	0.514987i	$0.172203\pi$
$942$	−5.68080e9	−	4.12735e9i	−0.221428	−	0.160877i
$943$	9.58844e9			0.372355
$944$	2.34127e10	+	1.70103e10i	0.905834	+	0.658127i
$945$	−2.42155e8	+	6.77698e10i	−0.00933429	+	2.61231i
$946$	1.78063e9	−	1.29370e9i	0.0683838	−	0.0496838i
$947$	−2.35443e10	+	1.71059e10i	−0.900868	+	0.654519i	−0.938689	−	0.344766i	$-0.887958\pi$
$947$	−2.35443e10	+	1.71059e10i	−0.900868	+	0.654519i	0.0378209	+	0.999285i	$0.487958\pi$
$948$	−1.33496e10	−	4.10858e10i	−0.508908	−	1.56626i
$949$	−1.81923e10			−0.690966
$950$	3.03817e9	−	2.17436e9i	0.114969	−	0.0822809i
$951$	−4.33980e8			−0.0163620
$952$	−1.41929e9	−	4.36812e9i	−0.0533140	−	0.164084i
$953$	4.36332e9	−	3.17013e9i	0.163302	−	0.118646i	−0.503133	−	0.864209i	$-0.667819\pi$
$953$	4.36332e9	−	3.17013e9i	0.163302	−	0.118646i	0.666435	+	0.745563i	$0.267819\pi$
$954$	4.25348e7	−	3.09034e7i	0.00158608	−	0.00115235i
$955$	2.60160e10	−	3.55402e10i	0.966559	−	1.32041i
$956$	3.26942e10	+	2.37538e10i	1.21023	+	0.879285i
$957$	−2.13394e10			−0.787029
$958$	3.00205e9	+	2.18111e9i	0.110316	+	0.0801492i
$959$	−9.37409e9	+	2.88505e10i	−0.343213	+	1.05630i
$960$	−2.58597e10	−	3.58616e10i	−0.943352	−	1.30822i
$961$	−8.19387e8	−	2.52182e9i	−0.0297822	−	0.0916603i
$962$	4.18997e8	−	1.28954e9i	0.0151739	−	0.0467006i
$963$	−3.00961e10	+	9.26262e10i	−1.08597	+	3.34227i
$964$	8.83802e8	+	2.72006e9i	0.0317750	+	0.0977934i
$965$	−2.83670e9	−	9.32918e8i	−0.101617	−	0.0334193i
$966$	8.49015e8	−	2.61300e9i	0.0303037	−	0.0932652i
$967$	−4.32930e10	−	3.14542e10i	−1.53966	−	1.11863i	−0.950549	−	0.310576i	$-0.899478\pi$
$967$	−4.32930e10	−	3.14542e10i	−1.53966	−	1.11863i	−0.589111	−	0.808052i	$-0.700522\pi$
$968$	−8.34418e8			−0.0295679
$969$	−3.04058e10	−	2.20911e10i	−1.07355	−	0.779982i
$970$	1.49901e9	+	2.07879e9i	0.0527356	+	0.0731325i
$971$	−1.24295e10	+	9.03057e9i	−0.435699	+	0.316554i	−0.783924	−	0.620857i	$-0.786785\pi$
$971$	−1.24295e10	+	9.03057e9i	−0.435699	+	0.316554i	0.348224	+	0.937411i	$0.386785\pi$
$972$	5.67828e9	−	4.12551e9i	0.198328	−	0.144094i
$973$	1.53203e10	+	4.71512e10i	0.533179	+	1.64096i
$974$	8.91813e8			0.0309255
$975$	−9.01964e9	+	2.70991e10i	−0.311654	+	0.936352i
$976$	−3.21261e10			−1.10607
$977$	1.85049e9	+	5.69523e9i	0.0634828	+	0.195380i	0.977767	−	0.209692i	$-0.0672463\pi$
$977$	1.85049e9	+	5.69523e9i	0.0634828	+	0.195380i	−0.914285	+	0.405073i	$0.867246\pi$
$978$	3.28175e9	−	2.38433e9i	0.112181	−	0.0815043i
$979$	4.51162e10	−	3.27788e10i	1.53671	−	1.11649i
$980$	4.80157e10	−	1.54118e10i	1.62964	−	0.523072i
$981$	2.57635e10	+	1.87183e10i	0.871291	+	0.633030i
$982$	−3.19915e9			−0.107806
$983$	−1.96558e10	−	1.42808e10i	−0.660016	−	0.479530i	0.206652	−	0.978414i	$-0.433743\pi$
$983$	−1.96558e10	−	1.42808e10i	−0.660016	−	0.479530i	−0.866668	+	0.498885i	$0.833743\pi$
$984$	3.22428e9	−	9.92331e9i	0.107882	−	0.332027i
$985$	−1.26688e10	+	4.06635e9i	−0.422385	+	0.135575i
$986$	−2.09299e8	−	6.44156e8i	−0.00695341	−	0.0214004i
$987$	1.37974e10	−	4.24641e10i	0.456760	−	1.40576i
$988$	7.74056e9	−	2.38230e10i	0.255342	−	0.785863i
$989$	−2.68808e9	−	8.27306e9i	−0.0883599	−	0.271944i
$990$	−2.20369e7	+	6.16728e9i	−0.000721817	+	0.202009i
$991$	−3.83053e7	+	1.17892e8i	−0.00125026	+	0.00384792i	−0.951680	−	0.307092i	$-0.900644\pi$
$991$	−3.83053e7	+	1.17892e8i	−0.00125026	+	0.00384792i	0.950429	+	0.310940i	$0.100644\pi$
$992$	6.84825e9	+	4.97554e9i	0.222735	+	0.161827i
$993$	1.18779e10			0.384963
$994$	−4.34211e8	−	3.15472e8i	−0.0140232	−	0.0101885i
$995$	−6.17763e9	−	2.03167e9i	−0.198811	−	0.0653840i
$996$	−3.48379e10	+	2.53112e10i	−1.11723	+	0.811718i
$997$	3.15015e10	−	2.28872e10i	1.00670	−	0.731407i	0.0431823	−	0.999067i	$-0.486250\pi$
$997$	3.15015e10	−	2.28872e10i	1.00670	−	0.731407i	0.963513	+	0.267660i	$0.0862504\pi$
$998$	−1.40937e9	−	4.33760e9i	−0.0448816	−	0.138131i
$999$	4.33727e10			1.37638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.6.10	✓	68
25.11	even	5		625.8.a.d.1.18		34
25.14	even	10		625.8.a.c.1.17		34
25.21	even	5	inner	25.8.d.a.21.10	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.6.10	✓	68	1.1	even	1	trivial
25.8.d.a.21.10	yes	68	25.21	even	5	inner
625.8.a.c.1.17		34	25.14	even	10
625.8.a.d.1.18		34	25.11	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.341871 + 1.05217i) q^{2} +(64.7040 - 47.0102i) q^{3} +(102.564 - 74.5171i) q^{4} +(265.518 + 87.3222i) q^{5} +(71.5832 + 52.0083i) q^{6} -1498.89 q^{7} +(228.032 + 165.675i) q^{8} +(1300.83 - 4003.53i) q^{9} +O(q^{10})\)	\(q+(0.341871 + 1.05217i) q^{2} +(64.7040 - 47.0102i) q^{3} +(102.564 - 74.5171i) q^{4} +(265.518 + 87.3222i) q^{5} +(71.5832 + 52.0083i) q^{6} -1498.89 q^{7} +(228.032 + 165.675i) q^{8} +(1300.83 - 4003.53i) q^{9} +(-1.10492 + 309.224i) q^{10} +(1464.09 + 4505.99i) q^{11} +(3133.23 - 9643.10i) q^{12} +(-1412.50 + 4347.23i) q^{13} +(-512.427 - 1577.09i) q^{14} +(21285.1 - 6831.96i) q^{15} +(4918.16 - 15136.5i) q^{16} +(8795.02 + 6389.96i) q^{17} +4657.12 q^{18} +(-34970.7 - 25407.7i) q^{19} +(33739.6 - 10829.5i) q^{20} +(-96984.1 + 70463.1i) q^{21} +(-4240.55 + 3080.94i) q^{22} +(6401.66 + 19702.3i) q^{23} +22543.0 q^{24} +(62874.7 + 46371.2i) q^{25} -5056.93 q^{26} +(-49986.9 - 153844. i) q^{27} +(-153732. + 111693. i) q^{28} +(-45559.9 + 33101.2i) q^{29} +(14465.2 + 20059.9i) q^{30} +(127561. + 92678.3i) q^{31} +53686.2 q^{32} +(306560. + 222729. i) q^{33} +(-3716.57 + 11438.4i) q^{34} +(-397982. - 130886. i) q^{35} +(-164913. - 507551. i) q^{36} +(-82856.0 + 255005. i) q^{37} +(14777.8 - 45481.3i) q^{38} +(112970. + 347685. i) q^{39} +(46079.6 + 63902.1i) q^{40} +(143028. - 440194. i) q^{41} +(-107295. - 77954.6i) q^{42} -419904. q^{43} +(485936. + 353053. i) q^{44} +(694989. - 949418. i) q^{45} +(-18541.6 + 13471.3i) q^{46} +(-301322. + 218923. i) q^{47} +(-393347. - 1.21060e6i) q^{48} +1.42313e6 q^{49} +(-27295.5 + 82008.0i) q^{50} +869466. q^{51} +(179071. + 551125. i) q^{52} +(9133.30 - 6635.73i) q^{53} +(144781. - 105190. i) q^{54} +(-4731.88 + 1.32427e6i) q^{55} +(-341795. - 248329. i) q^{56} -3.45716e6 q^{57} +(-50403.8 - 36620.5i) q^{58} +(-561895. + 1.72933e6i) q^{59} +(1.67399e6 - 2.28682e6i) q^{60} +(-623763. - 1.91975e6i) q^{61} +(-53904.2 + 165900. i) q^{62} +(-1.94979e6 + 6.00085e6i) q^{63} +(-611171. - 1.88099e6i) q^{64} +(-754654. + 1.03093e6i) q^{65} +(-129545. + 398698. i) q^{66} +(-206291. - 149879. i) q^{67} +1.37821e6 q^{68} +(1.34042e6 + 973872. i) q^{69} +(1656.15 - 463492. i) q^{70} +(261849. - 190244. i) q^{71} +(959916. - 697420. i) q^{72} +(1.22989e6 + 3.78520e6i) q^{73} -296635. q^{74} +(6.24816e6 + 44652.4i) q^{75} -5.48004e6 q^{76} +(-2.19450e6 - 6.75399e6i) q^{77} +(-327203. + 237727. i) q^{78} +(3.44694e6 - 2.50434e6i) q^{79} +(2.62762e6 - 3.58956e6i) q^{80} +(-3.01853e6 - 2.19309e6i) q^{81} +512057. q^{82} +(-3.43591e6 - 2.49633e6i) q^{83} +(-4.69637e6 + 1.44539e7i) q^{84} +(1.77725e6 + 2.46465e6i) q^{85} +(-143553. - 441811. i) q^{86} +(-1.39181e6 + 4.28356e6i) q^{87} +(-412673. + 1.27008e6i) q^{88} +(-3.63725e6 - 1.11943e7i) q^{89} +(1.23655e6 + 406669. i) q^{90} +(2.11718e6 - 6.51602e6i) q^{91} +(2.12474e6 + 1.54371e6i) q^{92} +1.26105e7 q^{93} +(-333358. - 242199. i) q^{94} +(-7.06669e6 - 9.79992e6i) q^{95} +(3.47371e6 - 2.52380e6i) q^{96} +(6.70521e6 - 4.87162e6i) q^{97} +(486526. + 1.49737e6i) q^{98} +1.99444e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9}+O(q^{10}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16} + 71504 q^{17} + 116208 q^{18} - 48685 q^{19} - 138265 q^{20} - 2274 q^{21} - 271952 q^{22} - 63227 q^{23} + 553980 q^{24} + 276615 q^{25} + 675246 q^{26} - 270235 q^{27} - 782613 q^{28} - 99655 q^{29} - 1011285 q^{30} + 39051 q^{31} + 1045974 q^{32} + 1766456 q^{33} + 605893 q^{34} - 476935 q^{35} - 2928227 q^{36} + 83909 q^{37} + 1937525 q^{38} + 1316257 q^{39} + 2903410 q^{40} - 1964944 q^{41} - 3462547 q^{42} - 3439822 q^{43} - 3557652 q^{44} - 2121790 q^{45} + 2982521 q^{46} + 1663474 q^{47} + 1678378 q^{48} + 6584354 q^{49} + 408485 q^{50} + 3922076 q^{51} - 5301176 q^{52} + 788553 q^{53} - 6946145 q^{54} - 2630560 q^{55} - 415350 q^{56} - 14598410 q^{57} + 4727030 q^{58} - 3625740 q^{59} + 29158890 q^{60} - 4161559 q^{61} + 19658928 q^{62} + 2426738 q^{63} - 4408596 q^{64} - 2030220 q^{65} - 6985528 q^{66} + 8470434 q^{67} - 29099218 q^{68} - 360673 q^{69} - 22417320 q^{70} - 4808044 q^{71} + 25676065 q^{72} + 5517633 q^{73} + 14050068 q^{74} + 257240 q^{75} + 22502000 q^{76} - 9936772 q^{77} + 14948561 q^{78} - 5343505 q^{79} - 3987180 q^{80} - 5865817 q^{81} - 76614542 q^{82} - 645927 q^{83} + 5992628 q^{84} + 48268560 q^{85} - 27540609 q^{86} + 65370380 q^{87} - 3612320 q^{88} + 11153500 q^{89} + 7267975 q^{90} - 9123484 q^{91} - 33863736 q^{92} - 118704764 q^{93} - 30761227 q^{94} - 26382485 q^{95} + 1256206 q^{96} + 55538244 q^{97} + 102201752 q^{98} + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

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